Space of modular forms of level 2325, weight 2, and Character 2325.c

• Label: 2325.2.c
• Level: $2325$
• Weight: $2$
• Character orbit: 2325.c
• Rep. character: $\chi_{2325}(1024,\cdot)$
• Character field: $\Q$
• Dimension: $88$
• Newform subspaces: $18$
• Sturm bound: $640$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2325 = 3 \cdot 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2325.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 18 \)
Sturm bound:			\(640\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2325, [\chi])\).

	Total	New	Old
Modular forms	332	88	244
Cusp forms	308	88	220
Eisenstein series	24	0	24

Trace form

88 * q - 84 * q^4 - 88 * q^9 + 8 * q^11 - 4 * q^14 + 60 * q^16 + 8 * q^19 - 8 * q^26 + 32 * q^29 - 12 * q^31 + 56 * q^34 + 84 * q^36 + 16 * q^39 + 8 * q^44 - 48 * q^46 - 128 * q^49 - 8 * q^59 - 24 * q^61 + 8 * q^64 + 16 * q^66 + 8 * q^69 + 48 * q^71 - 32 * q^74 + 76 * q^76 - 64 * q^79 + 88 * q^81 - 16 * q^84 - 8 * q^86 - 16 * q^89 + 48 * q^91 - 48 * q^94 - 40 * q^96 - 8 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(2325, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2325.2.c.a	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None		✓			2325.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}+i q^{3}-2 q^{4}-2 q^{6}+4 i q^{7}+\cdots\)
2325.2.c.b	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None		✓			2325.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-i q^{3}-2 q^{4}+2 q^{6}-4 i q^{7}+\cdots\)
2325.2.c.c	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None					465.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}+4 i q^{7}+\cdots\)
2325.2.c.d	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None					465.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}-2 i q^{7}+\cdots\)
2325.2.c.e	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None		✓			2325.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+i q^{3}+q^{4}-q^{6}-2 i q^{7}+\cdots\)
2325.2.c.f	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None		✓			2325.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-i q^{3}+q^{4}+q^{6}+2 i q^{7}+\cdots\)
2325.2.c.g	$2325$	$2$	2325.c	5.b	$2$	$2$	$2$	$18.565$	\(\Q(\sqrt{-1}) \)	None		✓			2325.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-i q^{3}+2 q^{4}-q^{9}-3 q^{11}-2 i q^{12}+\cdots\)
2325.2.c.h	$2325$	$2$	2325.c	5.b	$2$	$4$	$4$	$18.565$	\(\Q(i, \sqrt{5})\)	None					93.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\)
2325.2.c.i	$2325$	$2$	2325.c	5.b	$2$	$4$	$4$	$18.565$	\(\Q(\zeta_{8})\)	None					465.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+\beta_1 q^{3}+(-2\beta_{3}-1)q^{4}+\cdots\)
2325.2.c.j	$2325$	$2$	2325.c	5.b	$2$	$4$	$4$	$18.565$	\(\Q(\zeta_{12})\)	None					465.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta_{2} q^{2}+\beta_1 q^{3}-q^{4}+\beta_{3} q^{6}+\cdots\)
2325.2.c.k	$2325$	$2$	2325.c	5.b	$2$	$6$	$6$	$18.565$	6.0.5089536.1	None					465.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{4}q^{3}+(-2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots\)
2325.2.c.l	$2325$	$2$	2325.c	5.b	$2$	$6$	$6$	$18.565$	6.0.350464.1	None					465.2.a.g	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)
2325.2.c.m	$2325$	$2$	2325.c	5.b	$2$	$6$	$6$	$18.565$	6.0.350464.1	None		✓			2325.2.a.t	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}-\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
2325.2.c.n	$2325$	$2$	2325.c	5.b	$2$	$6$	$6$	$18.565$	6.0.3356224.1	None					93.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots\)
2325.2.c.o	$2325$	$2$	2325.c	5.b	$2$	$6$	$6$	$18.565$	6.0.350464.1	None					465.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2325.2.c.p	$2325$	$2$	2325.c	5.b	$2$	$8$	$8$	$18.565$	8.0.4589249536.2	None					465.2.a.h	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{1}-\beta _{5})q^{2}-\beta _{5}q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
2325.2.c.q	$2325$	$2$	2325.c	5.b	$2$	$12$	$12$	$18.565$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			2325.2.a.z	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(-1+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots\)
2325.2.c.r	$2325$	$2$	2325.c	5.b	$2$	$12$	$12$	$18.565$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			2325.2.a.y	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-1-\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2325, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2325, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(775, [\chi])\)\(^{\oplus 2}\)