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

\( 76 q - 86 q^{4} + O(q^{10}) \)

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	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		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2q^{4}-2iq^{7}-q^{11}-4iq^{13}+\cdots\)
2475.2.c.b	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+2iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.c	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-3iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.d	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-4iq^{7}+3iq^{8}-q^{11}+\cdots\)
2475.2.c.e	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+3iq^{7}+3iq^{8}+q^{11}+\cdots\)
2475.2.c.f	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+3iq^{8}+q^{11}+2iq^{13}+\cdots\)
2475.2.c.g	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}-2iq^{7}+3iq^{8}+q^{11}+\cdots\)
2475.2.c.h	$2475$	$2$	2475.c	5.b	$2$	$2$	$2$	$19.763$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+iq^{7}+q^{11}-iq^{13}+4q^{16}+\cdots\)
2475.2.c.i	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.j	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}+\beta _{2}q^{7}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
2475.2.c.k	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{7}+\cdots\)
2475.2.c.l	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}+(\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
2475.2.c.m	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(-1-\zeta_{8}^{3})q^{4}-2\zeta_{8}^{2}q^{7}+\cdots\)
2475.2.c.n	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{2}q^{2}-q^{4}+\zeta_{12}q^{7}+\zeta_{12}^{2}q^{8}+\cdots\)
2475.2.c.o	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
2475.2.c.p	$2475$	$2$	2475.c	5.b	$2$	$4$	$4$	$19.763$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(3\beta _{1}+2\beta _{3})q^{7}+\cdots\)
2475.2.c.q	$2475$	$2$	2475.c	5.b	$2$	$6$	$6$	$19.763$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4})q^{2}+(-3-\beta _{1})q^{4}+(\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.r	$2475$	$2$	2475.c	5.b	$2$	$6$	$6$	$19.763$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-2+\beta _{3})q^{4}+(-\beta _{2}-\beta _{5})q^{7}+\cdots\)
2475.2.c.s	$2475$	$2$	2475.c	5.b	$2$	$8$	$8$	$19.763$	8.0.9488318464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
2475.2.c.t	$2475$	$2$	2475.c	5.b	$2$	$8$	$8$	$19.763$	8.0.9488318464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2+\beta _{2})q^{4}+(\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \)