LMFDB - Space of modular forms of level 7350, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7350.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 99 $
Sturm bound:			$3360$
Trace bound:			$17$
Distinguishing $T_p$:			$11$, $13$, $17$, $19$, $23$, $31$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(7350))$.

	Total	New	Old
Modular forms	1776	131	1645
Cusp forms	1585	131	1454
Eisenstein series	191	0	191

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

$2$	$3$	$5$	$7$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$5$	$7$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$102$	$7$	$95$	$91$	$7$	$84$	$11$	$0$	$11$
$+$	$+$	$+$	$-$	$-$	$117$	$8$	$109$	$105$	$8$	$97$	$12$	$0$	$12$
$+$	$+$	$-$	$+$	$-$	$118$	$10$	$108$	$106$	$10$	$96$	$12$	$0$	$12$
$+$	$+$	$-$	$-$	$+$	$106$	$7$	$99$	$94$	$7$	$87$	$12$	$0$	$12$
$+$	$-$	$+$	$+$	$-$	$114$	$7$	$107$	$102$	$7$	$95$	$12$	$0$	$12$
$+$	$-$	$+$	$-$	$+$	$111$	$8$	$103$	$99$	$8$	$91$	$12$	$0$	$12$
$+$	$-$	$-$	$+$	$+$	$110$	$9$	$101$	$98$	$9$	$89$	$12$	$0$	$12$
$+$	$-$	$-$	$-$	$-$	$110$	$9$	$101$	$98$	$9$	$89$	$12$	$0$	$12$
$-$	$+$	$+$	$+$	$-$	$114$	$8$	$106$	$102$	$8$	$94$	$12$	$0$	$12$
$-$	$+$	$+$	$-$	$+$	$108$	$7$	$101$	$96$	$7$	$89$	$12$	$0$	$12$
$-$	$+$	$-$	$+$	$+$	$110$	$8$	$102$	$98$	$8$	$90$	$12$	$0$	$12$
$-$	$+$	$-$	$-$	$-$	$113$	$10$	$103$	$101$	$10$	$91$	$12$	$0$	$12$
$-$	$-$	$+$	$+$	$+$	$114$	$6$	$108$	$102$	$6$	$96$	$12$	$0$	$12$
$-$	$-$	$+$	$-$	$-$	$108$	$10$	$98$	$96$	$10$	$86$	$12$	$0$	$12$
$-$	$-$	$-$	$+$	$-$	$106$	$11$	$95$	$94$	$11$	$83$	$12$	$0$	$12$
$-$	$-$	$-$	$-$	$+$	$115$	$6$	$109$	$103$	$6$	$97$	$12$	$0$	$12$
Plus space				$+$	$876$	$58$	$818$	$781$	$58$	$723$	$95$	$0$	$95$
Minus space				$-$	$900$	$73$	$827$	$804$	$73$	$731$	$96$	$0$	$96$

Trace form

$ 131 q + q^{2} + q^{3} + 131 q^{4} - q^{6} + q^{8} + 131 q^{9} - 12 q^{11} + q^{12} + 6 q^{13} + 131 q^{16} - 6 q^{17} + q^{18} + 4 q^{19} - 4 q^{22} - 24 q^{23} - q^{24} - 22 q^{26} + q^{27} - 30 q^{29}+ \cdots - 12 q^{99}+O(q^{100}) $

131 * q + q^2 + q^3 + 131 * q^4 - q^6 + q^8 + 131 * q^9 - 12 * q^11 + q^12 + 6 * q^13 + 131 * q^16 - 6 * q^17 + q^18 + 4 * q^19 - 4 * q^22 - 24 * q^23 - q^24 - 22 * q^26 + q^27 - 30 * q^29 - 8 * q^31 + q^32 - 10 * q^34 + 131 * q^36 - 42 * q^37 - 12 * q^38 - 10 * q^39 - 50 * q^41 - 44 * q^43 - 12 * q^44 - 16 * q^47 + q^48 - 6 * q^51 + 6 * q^52 + 38 * q^53 - q^54 - 20 * q^57 + 30 * q^58 - 4 * q^59 - 14 * q^61 - 8 * q^62 + 131 * q^64 - 4 * q^66 - 36 * q^67 - 6 * q^68 - 8 * q^69 - 16 * q^71 + q^72 + 6 * q^73 + 10 * q^74 + 4 * q^76 - 6 * q^78 - 20 * q^79 + 131 * q^81 + 10 * q^82 + 28 * q^83 - 12 * q^86 - 22 * q^87 - 4 * q^88 + 14 * q^89 - 24 * q^92 - 16 * q^93 - 16 * q^94 - q^96 + 6 * q^97 - 12 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(7350))$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs				Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	7	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7350.2.a.a	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.b	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.b	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.n.a	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.c	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.a	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.d	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.d	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.e	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.d	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.f	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.g	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.g.a	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.h	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.j	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.i	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.f	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.j	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.a	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.k	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.g	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.l	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.l	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.m	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.g.c	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.n	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.h	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.o	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.a.n	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.p	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.a.c	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.q	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				42.2.e.a	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.r	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.j	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.s	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.c	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.t	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.n.a	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.u	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.b	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.v	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.d	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.w	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.a.e	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.x	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.d	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.y	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.a	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.z	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.j	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.ba	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.a	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bb	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.h	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bc	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.g.c	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bd	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.a.d	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.be	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.l	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bf	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.g	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bg	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				30.2.c.a	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bh	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.a.n	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bi	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.b	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bj	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.e	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bk	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.g.b	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bl	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				42.2.e.a	$1$	$0$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bm	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.c	$1$	$1$	$-1$	$1$	$0$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.bn	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.n.a	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bo	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.a.a	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bp	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.a	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bq	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.d	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.br	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				294.2.a.b	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bs	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.d	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bt	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.j	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bu	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.d	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bv	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.g	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bw	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.l	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bx	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.g.c	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.by	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.h	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.bz	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.g.b	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ca	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.e	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cb	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.b	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cc	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				30.2.c.a	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cd	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.c	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ce	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				42.2.e.b	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cf	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.a.c	$1$	$1$	$1$	$-1$	$0$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cg	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.c	$1$	$0$	$1$	$-1$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ch	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.n.a	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ci	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.d	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cj	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				294.2.a.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ck	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.d	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cl	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.a	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cm	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.f	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cn	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.j	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.co	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.g.a	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cp	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.d	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cq	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.h	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cr	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.g.c	$1$	$1$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cs	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.a.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.ct	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				30.2.a.a	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cu	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓	✓			7350.2.a.l	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cv	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.g	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cw	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				42.2.e.b	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cx	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				210.2.i.c	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cy	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.i.c	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.cz	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1050.2.a.j	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.da	$7350$	$2$	7350.a	1.a	$1$	$1$	$1$	$58.690$	$\Q$	None	✓				1470.2.a.c	$1$	$0$	$1$	$1$	$0$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.db	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.db	$1$	$0$	$-2$	$-2$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dc	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.dc	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dd	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓				1470.2.a.u	$1$	$1$	$-2$	$-2$	$0$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.de	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.db	$1$	$1$	$-2$	$2$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.df	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓				1470.2.a.u	$1$	$0$	$-2$	$2$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dg	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.dc	$1$	$0$	$-2$	$2$	$0$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dh	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓				1470.2.a.s	$1$	$0$	$2$	$-2$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.di	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.db	$1$	$0$	$2$	$-2$	$0$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dj	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.dc	$1$	$1$	$2$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dk	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.db	$1$	$1$	$2$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dl	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓				1470.2.a.s	$1$	$1$	$2$	$2$	$0$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dm	$7350$	$2$	7350.a	1.a	$1$	$2$	$2$	$58.690$	$\Q(\sqrt{2}) $	None	✓	✓			7350.2.a.dc	$1$	$0$	$2$	$2$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dn	$7350$	$2$	7350.a	1.a	$1$	$3$	$3$	$58.690$	3.3.2700.1	None	✓				210.2.n.b	$1$	$0$	$-3$	$-3$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.do	$7350$	$2$	7350.a	1.a	$1$	$3$	$3$	$58.690$	3.3.2700.1	None	✓		✓		210.2.n.b	$1$	$0$	$-3$	$3$	$0$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dp	$7350$	$2$	7350.a	1.a	$1$	$3$	$3$	$58.690$	3.3.2700.1	None	✓		✓		210.2.n.b	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dq	$7350$	$2$	7350.a	1.a	$1$	$3$	$3$	$58.690$	3.3.2700.1	None	✓				210.2.n.b	$1$	$0$	$3$	$3$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.dr	$7350$	$2$	7350.a	1.a	$1$	$4$	$4$	$58.690$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓		✓		1470.2.g.j	$1$	$0$	$-4$	$-4$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.ds	$7350$	$2$	7350.a	1.a	$1$	$4$	$4$	$58.690$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓		✓		1470.2.g.j	$1$	$1$	$-4$	$4$	$0$	$0$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
7350.2.a.dt	$7350$	$2$	7350.a	1.a	$1$	$4$	$4$	$58.690$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓		✓		1470.2.g.j	$1$	$1$	$4$	$-4$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
7350.2.a.du	$7350$	$2$	7350.a	1.a	$1$	$4$	$4$	$58.690$	$\Q(\sqrt{17 +8 \sqrt{2}})$	None	✓		✓		1470.2.g.j	$1$	$0$	$4$	$4$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(7350))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7350.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 99 \)
Sturm bound:			\(3360\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(11\), \(13\), \(17\), \(19\), \(23\), \(31\)

\(2\)	\(3\)	\(5\)	\(7\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(5\)	\(7\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(102\)	\(7\)	\(95\)	\(91\)	\(7\)	\(84\)	\(11\)	\(0\)	\(11\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(117\)	\(8\)	\(109\)	\(105\)	\(8\)	\(97\)	\(12\)	\(0\)	\(12\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(118\)	\(10\)	\(108\)	\(106\)	\(10\)	\(96\)	\(12\)	\(0\)	\(12\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(106\)	\(7\)	\(99\)	\(94\)	\(7\)	\(87\)	\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(114\)	\(7\)	\(107\)	\(102\)	\(7\)	\(95\)	\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(111\)	\(8\)	\(103\)	\(99\)	\(8\)	\(91\)	\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(110\)	\(9\)	\(101\)	\(98\)	\(9\)	\(89\)	\(12\)	\(0\)	\(12\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(110\)	\(9\)	\(101\)	\(98\)	\(9\)	\(89\)	\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(114\)	\(8\)	\(106\)	\(102\)	\(8\)	\(94\)	\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(108\)	\(7\)	\(101\)	\(96\)	\(7\)	\(89\)	\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(110\)	\(8\)	\(102\)	\(98\)	\(8\)	\(90\)	\(12\)	\(0\)	\(12\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(113\)	\(10\)	\(103\)	\(101\)	\(10\)	\(91\)	\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(114\)	\(6\)	\(108\)	\(102\)	\(6\)	\(96\)	\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(108\)	\(10\)	\(98\)	\(96\)	\(10\)	\(86\)	\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(106\)	\(11\)	\(95\)	\(94\)	\(11\)	\(83\)	\(12\)	\(0\)	\(12\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(115\)	\(6\)	\(109\)	\(103\)	\(6\)	\(97\)	\(12\)	\(0\)	\(12\)
Plus space				\(+\)	\(876\)	\(58\)	\(818\)	\(781\)	\(58\)	\(723\)	\(95\)	\(0\)	\(95\)
Minus space				\(-\)	\(900\)	\(73\)	\(827\)	\(804\)	\(73\)	\(731\)	\(96\)	\(0\)	\(96\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7350))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7350))\) into lower level spaces

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	7350.2.a

Level	$7350$
Weight	$2$
Character orbit	7350.a
Rep. character	$\chi_{7350}(1,\cdot)$
Character field	$\Q$
Dimension	$131$
Newform subspaces	$99$
Sturm bound	$3360$
Trace bound	$17$