LMFDB - Space of modular forms of level 9114, weight 2, and trivial character

Defining parameters

Level:	$ N $	$=$	$ 9114 = 2 \cdot 3 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9114.a (trivial)
Character field:			$\Q$
Newform subspaces:			$ 63 $
Sturm bound:			$3584$
Trace bound:			$13$
Distinguishing $T_p$:			$5$, $11$, $13$, $17$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_0(9114))$.

	Total	New	Old
Modular forms	1824	206	1618
Cusp forms	1761	206	1555
Eisenstein series	63	0	63

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

$2$	$3$	$7$	$31$	Fricke	Total			Cusp			Eisenstein
$2$	$3$	$7$	$31$	Fricke	All	New	Old	All	New	Old	All	New	Old
$+$	$+$	$+$	$+$	$+$	$104$	$11$	$93$	$101$	$11$	$90$	$3$	$0$	$3$
$+$	$+$	$+$	$-$	$-$	$120$	$15$	$105$	$116$	$15$	$101$	$4$	$0$	$4$
$+$	$+$	$-$	$+$	$-$	$121$	$14$	$107$	$117$	$14$	$103$	$4$	$0$	$4$
$+$	$+$	$-$	$-$	$+$	$109$	$11$	$98$	$105$	$11$	$94$	$4$	$0$	$4$
$+$	$-$	$+$	$+$	$-$	$116$	$15$	$101$	$112$	$15$	$97$	$4$	$0$	$4$
$+$	$-$	$+$	$-$	$+$	$116$	$11$	$105$	$112$	$11$	$101$	$4$	$0$	$4$
$+$	$-$	$-$	$+$	$+$	$111$	$11$	$100$	$107$	$11$	$96$	$4$	$0$	$4$
$+$	$-$	$-$	$-$	$-$	$115$	$14$	$101$	$111$	$14$	$97$	$4$	$0$	$4$
$-$	$+$	$+$	$+$	$-$	$120$	$17$	$103$	$116$	$17$	$99$	$4$	$0$	$4$
$-$	$+$	$+$	$-$	$+$	$108$	$9$	$99$	$104$	$9$	$95$	$4$	$0$	$4$
$-$	$+$	$-$	$+$	$+$	$110$	$10$	$100$	$106$	$10$	$96$	$4$	$0$	$4$
$-$	$+$	$-$	$-$	$-$	$118$	$16$	$102$	$114$	$16$	$98$	$4$	$0$	$4$
$-$	$-$	$+$	$+$	$+$	$116$	$9$	$107$	$112$	$9$	$103$	$4$	$0$	$4$
$-$	$-$	$+$	$-$	$-$	$112$	$17$	$95$	$108$	$17$	$91$	$4$	$0$	$4$
$-$	$-$	$-$	$+$	$-$	$114$	$16$	$98$	$110$	$16$	$94$	$4$	$0$	$4$
$-$	$-$	$-$	$-$	$+$	$114$	$10$	$104$	$110$	$10$	$100$	$4$	$0$	$4$
Plus space				$+$	$888$	$82$	$806$	$857$	$82$	$775$	$31$	$0$	$31$
Minus space				$-$	$936$	$124$	$812$	$904$	$124$	$780$	$32$	$0$	$32$

Trace form

$ 206 q + 2 q^{2} + 206 q^{4} - 4 q^{5} + 2 q^{8} + 206 q^{9} - 16 q^{11} + 12 q^{13} + 8 q^{15} + 206 q^{16} + 4 q^{17} + 2 q^{18} + 4 q^{19} - 4 q^{20} + 214 q^{25} + 4 q^{26} + 20 q^{29} + 2 q^{32} + 4 q^{33}+ \cdots - 16 q^{99}+O(q^{100}) $

206 * q + 2 * q^2 + 206 * q^4 - 4 * q^5 + 2 * q^8 + 206 * q^9 - 16 * q^11 + 12 * q^13 + 8 * q^15 + 206 * q^16 + 4 * q^17 + 2 * q^18 + 4 * q^19 - 4 * q^20 + 214 * q^25 + 4 * q^26 + 20 * q^29 + 2 * q^32 + 4 * q^33 + 4 * q^34 + 206 * q^36 + 4 * q^37 + 12 * q^41 + 8 * q^43 - 16 * q^44 - 4 * q^45 - 8 * q^46 - 8 * q^47 + 78 * q^50 - 12 * q^51 + 12 * q^52 + 84 * q^53 + 24 * q^55 + 16 * q^57 + 60 * q^58 + 24 * q^59 + 8 * q^60 + 28 * q^61 + 206 * q^64 + 104 * q^65 - 8 * q^66 + 4 * q^67 + 4 * q^68 - 16 * q^69 - 8 * q^71 + 2 * q^72 - 4 * q^73 + 52 * q^74 + 4 * q^76 - 12 * q^78 - 24 * q^79 - 4 * q^80 + 206 * q^81 - 20 * q^82 - 32 * q^83 + 64 * q^85 - 32 * q^86 + 24 * q^87 - 44 * q^89 + 2 * q^93 - 28 * q^94 - 40 * q^95 + 24 * q^97 - 16 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_0(9114))$ 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	31	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
9114.2.a.a	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.i	$1$	$0$	$-1$	$-1$	$-3$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.b	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				186.2.a.b	$1$	$1$	$-1$	$-1$	$-3$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-3q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.c	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.c	$1$	$1$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.d	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.d	$1$	$2$	$-1$	$-1$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.e	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.f	$1$	$2$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
9114.2.a.f	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.g	$1$	$1$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
9114.2.a.g	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.h	$1$	$0$	$-1$	$-1$	$0$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
9114.2.a.h	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.d	$1$	$1$	$-1$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.i	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.i	$1$	$1$	$-1$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.j	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.e	$1$	$1$	$-1$	$-1$	$2$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.k	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.c	$1$	$1$	$-1$	$1$	$-4$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-4q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.l	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.i	$1$	$1$	$-1$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.m	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.b	$1$	$1$	$-1$	$1$	$-2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-2q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.n	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				186.2.a.a	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.o	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.c	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.p	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.a	$1$	$1$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.q	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.d	$1$	$0$	$-1$	$1$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+2q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.r	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.r	$1$	$2$	$1$	$-1$	$-4$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.s	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.p	$1$	$1$	$1$	$-1$	$-2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.t	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				186.2.a.c	$1$	$1$	$1$	$-1$	$-1$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.u	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.o	$1$	$0$	$1$	$-1$	$-1$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.v	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.n	$1$	$1$	$1$	$-1$	$2$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+2q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.w	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.m	$1$	$0$	$1$	$-1$	$3$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+3q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.x	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.l	$1$	$1$	$1$	$1$	$-2$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.y	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.k	$1$	$0$	$1$	$1$	$-1$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.z	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓				1302.2.a.j	$1$	$0$	$1$	$1$	$2$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.ba	$9114$	$2$	9114.a	1.a	$1$	$1$	$1$	$72.776$	$\Q$	None	✓	✓			9114.2.a.r	$1$	$0$	$1$	$1$	$4$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+4q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.bb	$9114$	$2$	9114.a	1.a	$1$	$2$	$2$	$72.776$	$\Q(\sqrt{33}) $	None	✓				1302.2.a.r	$1$	$0$	$-2$	$-2$	$3$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots$
9114.2.a.bc	$9114$	$2$	9114.a	1.a	$1$	$2$	$2$	$72.776$	$\Q(\sqrt{17}) $	None	✓				1302.2.a.q	$1$	$0$	$-2$	$2$	$1$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.bd	$9114$	$2$	9114.a	1.a	$1$	$2$	$2$	$72.776$	$\Q(\sqrt{2}) $	None	✓	✓			9114.2.a.bd	$1$	$1$	$2$	$-2$	$0$	$0$	$-$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
9114.2.a.be	$9114$	$2$	9114.a	1.a	$1$	$2$	$2$	$72.776$	$\Q(\sqrt{17}) $	None	✓				186.2.a.d	$1$	$1$	$2$	$2$	$-3$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta )q^{5}+q^{6}+\cdots$
9114.2.a.bf	$9114$	$2$	9114.a	1.a	$1$	$2$	$2$	$72.776$	$\Q(\sqrt{2}) $	None	✓	✓			9114.2.a.bd	$1$	$1$	$2$	$2$	$0$	$0$	$-$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{6}+q^{8}+q^{9}+\cdots$
9114.2.a.bg	$9114$	$2$	9114.a	1.a	$1$	$3$	$3$	$72.776$	3.3.892.1	None	✓	✓			9114.2.a.bg	$1$	$0$	$-3$	$-3$	$-2$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
9114.2.a.bh	$9114$	$2$	9114.a	1.a	$1$	$3$	$3$	$72.776$	3.3.961.1	None	✓				1302.2.a.s	$1$	$0$	$-3$	$3$	$-1$	$0$	$+$	$-$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.bi	$9114$	$2$	9114.a	1.a	$1$	$3$	$3$	$72.776$	3.3.892.1	None	✓	✓			9114.2.a.bg	$1$	$0$	$-3$	$3$	$2$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(1-\beta _{1})q^{5}-q^{6}+\cdots$
9114.2.a.bj	$9114$	$2$	9114.a	1.a	$1$	$3$	$3$	$72.776$	3.3.229.1	None	✓				1302.2.a.u	$1$	$0$	$3$	$-3$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.bk	$9114$	$2$	9114.a	1.a	$1$	$3$	$3$	$72.776$	3.3.733.1	None	✓				1302.2.a.t	$1$	$0$	$3$	$3$	$1$	$0$	$-$	$-$	$-$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.bl	$9114$	$2$	9114.a	1.a	$1$	$4$	$4$	$72.776$	$\Q(\zeta_{24})^+$	None	✓	✓			9114.2.a.bl	$1$	$1$	$4$	$-4$	$4$	$0$	$-$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{1})q^{5}-q^{6}+\cdots$
9114.2.a.bm	$9114$	$2$	9114.a	1.a	$1$	$4$	$4$	$72.776$	$\Q(\zeta_{24})^+$	None	✓	✓			9114.2.a.bl	$1$	$1$	$4$	$4$	$-4$	$0$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{1})q^{5}+q^{6}+\cdots$
9114.2.a.bn	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.240881.1	None	✓				1302.2.j.h	$1$	$1$	$-5$	$-5$	$-3$	$0$	$+$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(-\beta _{1}+\beta _{4})q^{5}+\cdots$
9114.2.a.bo	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.1970001.1	None	✓				1302.2.j.g	$1$	$0$	$-5$	$-5$	$-1$	$0$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.bp	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.403137.1	None	✓		✓		1302.2.j.e	$1$	$1$	$-5$	$-5$	$1$	$0$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+\beta _{4}q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.bq	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.574857.1	None	✓		✓		1302.2.j.f	$1$	$0$	$-5$	$-5$	$3$	$0$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(\beta _{1}-\beta _{2})q^{5}+q^{6}+\cdots$
9114.2.a.br	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.574857.1	None	✓				1302.2.j.f	$1$	$1$	$-5$	$5$	$-3$	$0$	$+$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots$
9114.2.a.bs	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.403137.1	None	✓				1302.2.j.e	$1$	$0$	$-5$	$5$	$-1$	$0$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-\beta _{4}q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.bt	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.1970001.1	None	✓		✓		1302.2.j.g	$1$	$1$	$-5$	$5$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.bu	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.240881.1	None	✓		✓		1302.2.j.h	$1$	$0$	$-5$	$5$	$3$	$0$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{4})q^{5}-q^{6}+\cdots$
9114.2.a.bv	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.369849.1	None	✓		✓		1302.2.j.d	$1$	$1$	$5$	$-5$	$-5$	$0$	$-$	$+$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots$
9114.2.a.bw	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.4590729.1	None	✓		✓		1302.2.j.a	$1$	$1$	$5$	$-5$	$-5$	$0$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(-1-\beta _{4})q^{5}-q^{6}+\cdots$
9114.2.a.bx	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.11978672.1	None	✓	✓			9114.2.a.bx	$1$	$0$	$5$	$-5$	$0$	$0$	$-$	$+$	$-$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.by	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.1426401.1	None	✓				1302.2.j.c	$1$	$0$	$5$	$-5$	$5$	$0$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1-\beta _{3}+\beta _{4})q^{5}+\cdots$
9114.2.a.bz	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.288385.1	None	✓				1302.2.j.b	$1$	$0$	$5$	$-5$	$5$	$0$	$-$	$+$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+(1+\beta _{3}-\beta _{4})q^{5}+\cdots$
9114.2.a.ca	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.1426401.1	None	✓		✓		1302.2.j.c	$1$	$1$	$5$	$5$	$-5$	$0$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1+\beta _{3}-\beta _{4})q^{5}+\cdots$
9114.2.a.cb	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.288385.1	None	✓		✓		1302.2.j.b	$1$	$1$	$5$	$5$	$-5$	$0$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(-1-\beta _{3}+\beta _{4})q^{5}+\cdots$
9114.2.a.cc	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.11978672.1	None	✓	✓			9114.2.a.bx	$1$	$0$	$5$	$5$	$0$	$0$	$-$	$-$	$-$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{8}+\cdots$
9114.2.a.cd	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.369849.1	None	✓				1302.2.j.d	$1$	$0$	$5$	$5$	$5$	$0$	$-$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots$
9114.2.a.ce	$9114$	$2$	9114.a	1.a	$1$	$5$	$5$	$72.776$	5.5.4590729.1	None	✓				1302.2.j.a	$1$	$0$	$5$	$5$	$5$	$0$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+(1+\beta _{4})q^{5}+q^{6}+\cdots$
9114.2.a.cf	$9114$	$2$	9114.a	1.a	$1$	$6$	$6$	$72.776$	6.6.10338304.1	None	✓	✓	✓		9114.2.a.cf	$1$	$1$	$-6$	$-6$	$4$	$0$	$+$	$+$	$+$	$+$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+(1+\beta _{5})q^{5}+q^{6}+\cdots$
9114.2.a.cg	$9114$	$2$	9114.a	1.a	$1$	$6$	$6$	$72.776$	6.6.10338304.1	None	✓	✓	✓		9114.2.a.cf	$1$	$1$	$-6$	$6$	$-4$	$0$	$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+(-1-\beta _{5})q^{5}-q^{6}+\cdots$
9114.2.a.ch	$9114$	$2$	9114.a	1.a	$1$	$10$	$10$	$72.776$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		9114.2.a.ch	$1$	$0$	$-10$	$-10$	$-4$	$0$	$+$	$+$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}+q^{6}-q^{8}+\cdots$
9114.2.a.ci	$9114$	$2$	9114.a	1.a	$1$	$10$	$10$	$72.776$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	None	✓	✓	✓		9114.2.a.ch	$1$	$0$	$-10$	$10$	$4$	$0$	$+$	$-$	$+$	$+$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}-q^{6}-q^{8}+\cdots$
9114.2.a.cj	$9114$	$2$	9114.a	1.a	$1$	$12$	$12$	$72.776$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		9114.2.a.cj	$1$	$0$	$12$	$-12$	$-4$	$0$	$-$	$+$	$+$	$+$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-\beta _{1}q^{5}-q^{6}+q^{8}+\cdots$
9114.2.a.ck	$9114$	$2$	9114.a	1.a	$1$	$12$	$12$	$72.776$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	None	✓	✓	✓		9114.2.a.cj	$1$	$0$	$12$	$12$	$4$	$0$	$-$	$-$	$+$	$-$	$-$	$2^{3}$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+\beta _{1}q^{5}+q^{6}+q^{8}+\cdots$

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_0(9114))$ 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:	\( N \)	\(=\)	\( 9114 = 2 \cdot 3 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9114.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 63 \)
Sturm bound:			\(3584\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\), \(13\), \(17\)

\(2\)	\(3\)	\(7\)	\(31\)	Fricke	Total			Cusp			Eisenstein
\(2\)	\(3\)	\(7\)	\(31\)	Fricke	All	New	Old	All	New	Old	All	New	Old
\(+\)	\(+\)	\(+\)	\(+\)	\(+\)	\(104\)	\(11\)	\(93\)	\(101\)	\(11\)	\(90\)	\(3\)	\(0\)	\(3\)
\(+\)	\(+\)	\(+\)	\(-\)	\(-\)	\(120\)	\(15\)	\(105\)	\(116\)	\(15\)	\(101\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(+\)	\(-\)	\(121\)	\(14\)	\(107\)	\(117\)	\(14\)	\(103\)	\(4\)	\(0\)	\(4\)
\(+\)	\(+\)	\(-\)	\(-\)	\(+\)	\(109\)	\(11\)	\(98\)	\(105\)	\(11\)	\(94\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(+\)	\(-\)	\(116\)	\(15\)	\(101\)	\(112\)	\(15\)	\(97\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(+\)	\(-\)	\(+\)	\(116\)	\(11\)	\(105\)	\(112\)	\(11\)	\(101\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(+\)	\(+\)	\(111\)	\(11\)	\(100\)	\(107\)	\(11\)	\(96\)	\(4\)	\(0\)	\(4\)
\(+\)	\(-\)	\(-\)	\(-\)	\(-\)	\(115\)	\(14\)	\(101\)	\(111\)	\(14\)	\(97\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(+\)	\(-\)	\(120\)	\(17\)	\(103\)	\(116\)	\(17\)	\(99\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(+\)	\(-\)	\(+\)	\(108\)	\(9\)	\(99\)	\(104\)	\(9\)	\(95\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(+\)	\(+\)	\(110\)	\(10\)	\(100\)	\(106\)	\(10\)	\(96\)	\(4\)	\(0\)	\(4\)
\(-\)	\(+\)	\(-\)	\(-\)	\(-\)	\(118\)	\(16\)	\(102\)	\(114\)	\(16\)	\(98\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(+\)	\(+\)	\(116\)	\(9\)	\(107\)	\(112\)	\(9\)	\(103\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(+\)	\(-\)	\(-\)	\(112\)	\(17\)	\(95\)	\(108\)	\(17\)	\(91\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(+\)	\(-\)	\(114\)	\(16\)	\(98\)	\(110\)	\(16\)	\(94\)	\(4\)	\(0\)	\(4\)
\(-\)	\(-\)	\(-\)	\(-\)	\(+\)	\(114\)	\(10\)	\(104\)	\(110\)	\(10\)	\(100\)	\(4\)	\(0\)	\(4\)
Plus space				\(+\)	\(888\)	\(82\)	\(806\)	\(857\)	\(82\)	\(775\)	\(31\)	\(0\)	\(31\)
Minus space				\(-\)	\(936\)	\(124\)	\(812\)	\(904\)	\(124\)	\(780\)	\(32\)	\(0\)	\(32\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Defining parameters

Dimensions

Trace form

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9114))\) into newform subspaces

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9114))\) 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	9114.2.a

Level	$9114$
Weight	$2$
Character orbit	9114.a
Rep. character	$\chi_{9114}(1,\cdot)$
Character field	$\Q$
Dimension	$206$
Newform subspaces	$63$
Sturm bound	$3584$
Trace bound	$13$