LMFDB - Space of modular forms of level 7098, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 73 $
Sturm bound:			$2912$
Trace bound:			$17$
Distinguishing $T_p$:			$5$, $11$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(7098))$.

	Total	New	Old
Modular forms	1512	154	1358
Cusp forms	1401	154	1247
Eisenstein series	111	0	111

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

$2$	$3$	$7$	$13$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$7$	$13$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$84$	$11$	$73$	$78$	$11$	$67$	$6$	$0$	$6$
$+$	$+$	$+$	$-$	$-$	$103$	$9$	$94$	$96$	$9$	$87$	$7$	$0$	$7$
$+$	$+$	$-$	$+$	$-$	$98$	$10$	$88$	$91$	$10$	$81$	$7$	$0$	$7$
$+$	$+$	$-$	$-$	$+$	$92$	$9$	$83$	$85$	$9$	$76$	$7$	$0$	$7$
$+$	$-$	$+$	$+$	$-$	$98$	$10$	$88$	$91$	$10$	$81$	$7$	$0$	$7$
$+$	$-$	$+$	$-$	$+$	$91$	$9$	$82$	$84$	$9$	$75$	$7$	$0$	$7$
$+$	$-$	$-$	$+$	$+$	$98$	$11$	$87$	$91$	$11$	$80$	$7$	$0$	$7$
$+$	$-$	$-$	$-$	$-$	$92$	$9$	$83$	$85$	$9$	$76$	$7$	$0$	$7$
$-$	$+$	$+$	$+$	$-$	$98$	$13$	$85$	$91$	$13$	$78$	$7$	$0$	$7$
$-$	$+$	$+$	$-$	$+$	$92$	$6$	$86$	$85$	$6$	$79$	$7$	$0$	$7$
$-$	$+$	$-$	$+$	$+$	$91$	$7$	$84$	$84$	$7$	$77$	$7$	$0$	$7$
$-$	$+$	$-$	$-$	$-$	$96$	$12$	$84$	$89$	$12$	$77$	$7$	$0$	$7$
$-$	$-$	$+$	$+$	$+$	$98$	$7$	$91$	$91$	$7$	$84$	$7$	$0$	$7$
$-$	$-$	$+$	$-$	$-$	$92$	$12$	$80$	$85$	$12$	$73$	$7$	$0$	$7$
$-$	$-$	$-$	$+$	$-$	$91$	$13$	$78$	$84$	$13$	$71$	$7$	$0$	$7$
$-$	$-$	$-$	$-$	$+$	$98$	$6$	$92$	$91$	$6$	$85$	$7$	$0$	$7$
Plus space				$+$	$744$	$66$	$678$	$689$	$66$	$623$	$55$	$0$	$55$
Minus space				$-$	$768$	$88$	$680$	$712$	$88$	$624$	$56$	$0$	$56$

Trace form

$ 154 q - 2 q^{2} + 154 q^{4} - 4 q^{5} - 2 q^{8} + 154 q^{9} - 4 q^{10} - 8 q^{11} - 8 q^{15} + 154 q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{20} + 2 q^{21} - 16 q^{23} + 134 q^{25} - 12 q^{29} - 16 q^{31} - 2 q^{32}+ \cdots - 8 q^{99}+O(q^{100}) $

154 * q - 2 * q^2 + 154 * q^4 - 4 * q^5 - 2 * q^8 + 154 * q^9 - 4 * q^10 - 8 * q^11 - 8 * q^15 + 154 * q^16 - 4 * q^17 - 2 * q^18 - 4 * q^20 + 2 * q^21 - 16 * q^23 + 134 * q^25 - 12 * q^29 - 16 * q^31 - 2 * q^32 - 20 * q^34 - 8 * q^35 + 154 * q^36 + 20 * q^37 - 4 * q^40 - 4 * q^41 - 2 * q^42 - 8 * q^43 - 8 * q^44 - 4 * q^45 + 8 * q^46 + 16 * q^47 + 154 * q^49 + 2 * q^50 - 28 * q^53 - 16 * q^55 + 24 * q^57 - 4 * q^58 - 32 * q^59 - 8 * q^60 + 12 * q^61 + 32 * q^62 + 154 * q^64 - 4 * q^68 + 8 * q^70 - 2 * q^72 + 28 * q^73 + 4 * q^74 + 32 * q^75 - 16 * q^77 - 16 * q^79 - 4 * q^80 + 154 * q^81 + 12 * q^82 + 16 * q^83 + 2 * q^84 + 40 * q^85 + 24 * q^86 + 12 * q^89 - 4 * q^90 - 16 * q^92 + 32 * q^93 + 16 * q^94 + 16 * q^95 + 44 * q^97 - 2 * q^98 - 8 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(7098))$ 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	7	13	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7098.2.a.a	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.b	$1$	$2$	$-1$	$-1$	$-3$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.b	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.e	$1$	$0$	$-1$	$-1$	$-3$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.c	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.f	$1$	$0$	$-1$	$-1$	$-2$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.d	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.a	$1$	$1$	$-1$	$-1$	$1$	$1$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.e	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.g	$1$	$1$	$-1$	$-1$	$2$	$-1$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.f	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				42.2.a.a	$1$	$0$	$-1$	$-1$	$2$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.g	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.h	$1$	$0$	$-1$	$-1$	$4$	$1$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+4q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.h	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.d	$1$	$0$	$-1$	$1$	$-2$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.i	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.c	$1$	$0$	$-1$	$1$	$-2$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.j	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.g	$1$	$0$	$-1$	$1$	$-2$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.k	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.b	$1$	$0$	$-1$	$1$	$-2$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.l	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.a	$1$	$0$	$-1$	$1$	$0$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots$
7098.2.a.m	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.e	$1$	$1$	$-1$	$1$	$0$	$1$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots$
7098.2.a.n	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.f	$1$	$0$	$-1$	$1$	$1$	$-1$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.o	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.c	$1$	$1$	$-1$	$1$	$1$	$-1$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.p	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.d	$1$	$0$	$-1$	$1$	$3$	$1$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+3q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.q	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.h	$1$	$0$	$1$	$-1$	$-4$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.r	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.g	$1$	$1$	$1$	$-1$	$-2$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.s	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.a	$1$	$1$	$1$	$-1$	$-1$	$-1$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.t	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.a	$1$	$1$	$1$	$-1$	$1$	$1$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.u	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.f	$1$	$0$	$1$	$-1$	$2$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.v	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.b	$1$	$0$	$1$	$-1$	$3$	$-1$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.w	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.d	$1$	$1$	$1$	$1$	$-3$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.x	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.d	$1$	$0$	$1$	$1$	$-3$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.y	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.c	$1$	$1$	$1$	$1$	$-1$	$1$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.z	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.c	$1$	$0$	$1$	$1$	$-1$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.ba	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.e	$1$	$1$	$1$	$1$	$0$	$-1$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}-q^{7}+q^{8}+\cdots$
7098.2.a.bb	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.a	$1$	$0$	$1$	$1$	$0$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots$
7098.2.a.bc	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.c.b	$1$	$0$	$1$	$1$	$2$	$-1$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.bd	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.c	$1$	$0$	$1$	$1$	$2$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.be	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.a.b	$1$	$0$	$1$	$1$	$2$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.bf	$7098$	$2$	7098.a	1.a	$1$	$1$	$1$	$56.678$	$\Q$	None	✓				546.2.l.d	$1$	$0$	$1$	$1$	$2$	$1$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.bg	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.c.e	$1$	$0$	$-2$	$-2$	$-3$	$-2$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
7098.2.a.bh	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{41}) $	None	✓				546.2.a.i	$1$	$1$	$-2$	$-2$	$1$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.bi	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.l.l	$1$	$1$	$-2$	$-2$	$1$	$-2$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.bj	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.d	$1$	$1$	$-2$	$-2$	$2$	$2$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
7098.2.a.bk	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{129}) $	None	✓				546.2.l.k	$1$	$0$	$-2$	$-2$	$4$	$2$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.bl	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.a.j	$1$	$1$	$-2$	$2$	$-3$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots$
7098.2.a.bm	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{57}) $	None	✓				546.2.l.j	$1$	$0$	$-2$	$2$	$-1$	$-2$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.bn	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.c	$1$	$0$	$-2$	$2$	$0$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2\beta q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.bo	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.b	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
7098.2.a.bp	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.a	$1$	$0$	$-2$	$2$	$2$	$2$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
7098.2.a.bq	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.l.i	$1$	$1$	$-2$	$2$	$3$	$2$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
7098.2.a.br	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{129}) $	None	✓				546.2.l.k	$1$	$0$	$2$	$-2$	$-4$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.bs	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.d	$1$	$1$	$2$	$-2$	$-2$	$-2$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1+\beta )q^{5}-q^{6}+\cdots$
7098.2.a.bt	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.l.l	$1$	$1$	$2$	$-2$	$-1$	$2$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta q^{5}-q^{6}+q^{7}+\cdots$
7098.2.a.bu	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{57}) $	None	✓				546.2.a.h	$1$	$0$	$2$	$-2$	$1$	$-2$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.bv	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.c.e	$1$	$0$	$2$	$-2$	$3$	$2$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}-q^{6}+\cdots$
7098.2.a.bw	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{17}) $	None	✓				546.2.l.i	$1$	$1$	$2$	$2$	$-3$	$-2$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
7098.2.a.bx	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.a	$1$	$0$	$2$	$2$	$-2$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots$
7098.2.a.by	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.b	$1$	$1$	$2$	$2$	$-2$	$2$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta )q^{5}+q^{6}+\cdots$
7098.2.a.bz	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{3}) $	None	✓				546.2.s.c	$1$	$0$	$2$	$2$	$0$	$-2$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2\beta q^{5}+q^{6}-q^{7}+\cdots$
7098.2.a.ca	$7098$	$2$	7098.a	1.a	$1$	$2$	$2$	$56.678$	$\Q(\sqrt{57}) $	None	✓				546.2.l.j	$1$	$0$	$2$	$2$	$1$	$2$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.cb	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓			7098.2.a.cb	$1$	$1$	$-3$	$-3$	$-3$	$3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2})q^{5}+\cdots$
7098.2.a.cc	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cc	$1$	$0$	$-3$	$-3$	$-2$	$3$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots$
7098.2.a.cd	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓			7098.2.a.cd	$1$	$1$	$-3$	$-3$	$0$	$3$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1-2\beta _{1}+\beta _{2})q^{5}+\cdots$
7098.2.a.ce	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓			7098.2.a.ce	$1$	$0$	$-3$	$-3$	$4$	$-3$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}+q^{6}+\cdots$
7098.2.a.cf	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cf	$1$	$0$	$-3$	$3$	$2$	$3$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
7098.2.a.cg	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cg	$1$	$0$	$-3$	$3$	$8$	$-3$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(3-\beta _{1})q^{5}-q^{6}+\cdots$
7098.2.a.ch	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.ce	$1$	$1$	$3$	$-3$	$-4$	$3$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta _{1})q^{5}-q^{6}+\cdots$
7098.2.a.ci	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓			7098.2.a.cd	$1$	$0$	$3$	$-3$	$0$	$-3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
7098.2.a.cj	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cc	$1$	$1$	$3$	$-3$	$2$	$-3$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
7098.2.a.ck	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓			7098.2.a.cb	$1$	$0$	$3$	$-3$	$3$	$-3$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{1}+\beta _{2})q^{5}+\cdots$
7098.2.a.cl	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cg	$1$	$1$	$3$	$3$	$-8$	$3$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-3-\beta _{2})q^{5}+q^{6}+\cdots$
7098.2.a.cm	$7098$	$2$	7098.a	1.a	$1$	$3$	$3$	$56.678$	$\Q(\zeta_{14})^+$	None	✓	✓	✓		7098.2.a.cf	$1$	$1$	$3$	$3$	$-2$	$-3$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta _{2})q^{5}+q^{6}+\cdots$
7098.2.a.cn	$7098$	$2$	7098.a	1.a	$1$	$4$	$4$	$56.678$	$\Q(\sqrt{17 +8 \sqrt{3}})$	None	✓		✓		546.2.s.e	$1$	$0$	$-4$	$-4$	$-6$	$-4$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1-\beta _{3})q^{5}+q^{6}+\cdots$
7098.2.a.co	$7098$	$2$	7098.a	1.a	$1$	$4$	$4$	$56.678$	$\Q(\sqrt{17 +8 \sqrt{3}})$	None	✓				546.2.s.e	$1$	$0$	$4$	$-4$	$6$	$4$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{3})q^{5}-q^{6}+\cdots$
7098.2.a.cp	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.8569169.1	None	✓	✓	✓		7098.2.a.cp	$1$	$1$	$-6$	$-6$	$3$	$-6$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+q^{6}+\cdots$
7098.2.a.cq	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.6148961.1	None	✓	✓	✓		7098.2.a.cq	$1$	$1$	$-6$	$6$	$-9$	$6$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-2+\beta _{5})q^{5}-q^{6}+\cdots$
7098.2.a.cr	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.48406561.1	None	✓	✓	✓		7098.2.a.cr	$1$	$1$	$-6$	$6$	$-3$	$-6$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{7}+\cdots$
7098.2.a.cs	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.8569169.1	None	✓	✓	✓		7098.2.a.cp	$1$	$0$	$6$	$-6$	$-3$	$6$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{5})q^{5}+\cdots$
7098.2.a.ct	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.48406561.1	None	✓	✓	✓		7098.2.a.cr	$1$	$0$	$6$	$6$	$3$	$6$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{7}+\cdots$
7098.2.a.cu	$7098$	$2$	7098.a	1.a	$1$	$6$	$6$	$56.678$	6.6.6148961.1	None	✓	✓	✓		7098.2.a.cq	$1$	$0$	$6$	$6$	$9$	$-6$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(2-\beta _{5})q^{5}+q^{6}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(7098))$ into lower level spaces

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$ over number fields
Genus 2 curves
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 73 \)
Sturm bound:			\(2912\)
Trace bound:			\(17\)
Distinguishing \(T_p\):			\(5\), \(11\), \(17\)

\(2\)	\(3\)	\(7\)	\(13\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(7\)	\(13\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(84\)	\(11\)	\(73\)	\(78\)	\(11\)	\(67\)	\(6\)	\(0\)	\(6\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(103\)	\(9\)	\(94\)	\(96\)	\(9\)	\(87\)	\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(98\)	\(10\)	\(88\)	\(91\)	\(10\)	\(81\)	\(7\)	\(0\)	\(7\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(92\)	\(9\)	\(83\)	\(85\)	\(9\)	\(76\)	\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(98\)	\(10\)	\(88\)	\(91\)	\(10\)	\(81\)	\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(91\)	\(9\)	\(82\)	\(84\)	\(9\)	\(75\)	\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(98\)	\(11\)	\(87\)	\(91\)	\(11\)	\(80\)	\(7\)	\(0\)	\(7\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(92\)	\(9\)	\(83\)	\(85\)	\(9\)	\(76\)	\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(98\)	\(13\)	\(85\)	\(91\)	\(13\)	\(78\)	\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(92\)	\(6\)	\(86\)	\(85\)	\(6\)	\(79\)	\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(91\)	\(7\)	\(84\)	\(84\)	\(7\)	\(77\)	\(7\)	\(0\)	\(7\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(96\)	\(12\)	\(84\)	\(89\)	\(12\)	\(77\)	\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(98\)	\(7\)	\(91\)	\(91\)	\(7\)	\(84\)	\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(92\)	\(12\)	\(80\)	\(85\)	\(12\)	\(73\)	\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(91\)	\(13\)	\(78\)	\(84\)	\(13\)	\(71\)	\(7\)	\(0\)	\(7\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(98\)	\(6\)	\(92\)	\(91\)	\(6\)	\(85\)	\(7\)	\(0\)	\(7\)
Plus space				\(+\)	\(744\)	\(66\)	\(678\)	\(689\)	\(66\)	\(623\)	\(55\)	\(0\)	\(55\)
Minus space				\(-\)	\(768\)	\(88\)	\(680\)	\(712\)	\(88\)	\(624\)	\(56\)	\(0\)	\(56\)

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Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7098))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7098))\) 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	7098.2.a

Level	$7098$
Weight	$2$
Character orbit	7098.a
Rep. character	$\chi_{7098}(1,\cdot)$
Character field	$\Q$
Dimension	$154$
Newform subspaces	$73$
Sturm bound	$2912$
Trace bound	$17$