Space of modular forms of level 2475, weight 2, and Character 2475.c

• Label: 2475.2.c
• Level: $2475$
• Weight: $2$
• Character orbit: 2475.c
• Rep. character: $\chi_{2475}(199,\cdot)$
• Character field: $\Q$
• Dimension: $76$
• Newform subspaces: $20$
• Sturm bound: $720$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2475.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 20 \)
Sturm bound:			\(720\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

	Total	New	Old
Modular forms	384	76	308
Cusp forms	336	76	260
Eisenstein series	48	0	48

Trace form

76 * q - 86 * q^4 - 4 * q^11 - 4 * q^14 + 98 * q^16 - 12 * q^19 - 8 * q^26 - 40 * q^29 + 22 * q^31 + 28 * q^34 + 40 * q^41 + 18 * q^44 - 72 * q^46 - 48 * q^49 + 36 * q^56 + 26 * q^59 + 12 * q^61 - 94 * q^64 - 98 * q^71 + 48 * q^74 - 12 * q^76 + 32 * q^79 - 16 * q^86 - 50 * q^89 - 76 * q^91 + 112 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
2475.2.c.a	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					11.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 q^{4}-2 i q^{7}-q^{11}+\cdots\)
2475.2.c.b	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					99.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+2 i q^{7}+3 i q^{8}-q^{11}+\cdots\)
2475.2.c.c	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		✓			2475.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-3 i q^{7}+3 i q^{8}-q^{11}+\cdots\)
2475.2.c.d	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					33.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-4 i q^{7}+3 i q^{8}-q^{11}+\cdots\)
2475.2.c.e	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		✓			2475.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{7}+3 i q^{8}+q^{11}+\cdots\)
2475.2.c.f	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					55.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}+3 i q^{8}+q^{11}+2 i q^{13}+\cdots\)
2475.2.c.g	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					99.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}+q^{4}-2 i q^{7}+3 i q^{8}+q^{11}+\cdots\)
2475.2.c.h	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None					825.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 q^{4}+i q^{7}+q^{11}-i q^{13}+4 q^{16}+\cdots\)
2475.2.c.i	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{17})\)	None		✓			2475.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.j	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{17})\)	None		✓			2475.2.a.p	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.k	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{13})\)	None					275.2.a.e	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2475.2.c.l	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None					55.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+(-\beta_{3}-1)q^{4}+(\beta_{2}+\beta_1)q^{7}+\cdots\)
2475.2.c.m	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None					165.2.a.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_1 q^{2}+(-\beta_{3}-1)q^{4}-2\beta_{2} q^{7}+\cdots\)
2475.2.c.n	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{12})\)	None					165.2.a.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta_{2} q^{2}-q^{4}+\beta_1 q^{7}+\beta_{2} q^{8}+\cdots\)
2475.2.c.o	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None					825.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta_{2}+\beta_1)q^{2}+(-2\beta_{3}-1)q^{4}+\cdots\)
2475.2.c.p	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{5})\)	None					275.2.a.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2475.2.c.q	$2475$	$2$	2475.c	5.b	$2$	$6$	$6$	$19.763$	6.0.5161984.1	None					825.2.a.i	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{2}+(-3-\beta _{1})q^{4}+(\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.r	$2475$	$2$	2475.c	5.b	$2$	$6$	$6$	$19.763$	6.0.350464.1	None					165.2.a.c	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
2475.2.c.s	$2475$	$2$	2475.c	5.b	$2$	$8$	$8$	$19.763$	8.0.9488318464.1	None					495.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.t	$2475$	$2$	2475.c	5.b	$2$	$8$	$8$	$19.763$	8.0.9488318464.1	None					495.2.a.f	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)