Space of modular forms of level 1275, weight 2, and Character 1275.d

• Label: 1275.2.d
• Level: $1275$
• Weight: $2$
• Character orbit: 1275.d
• Rep. character: $\chi_{1275}(424,\cdot)$
• Character field: $\Q$
• Dimension: $56$
• Newform subspaces: $10$
• Sturm bound: $360$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(360\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1275, [\chi])\).

	Total	New	Old
Modular forms	192	56	136
Cusp forms	168	56	112
Eisenstein series	24	0	24

Trace form

\( 56 q - 68 q^{4} + 56 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1275, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1275.2.d.a	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-q^{3}-2q^{4}-2iq^{6}+2q^{7}+\cdots\)
1275.2.d.b	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}+q^{4}-iq^{6}-4q^{7}+3iq^{8}+\cdots\)
1275.2.d.c	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+q^{3}-2q^{4}+2iq^{6}-2q^{7}+\cdots\)
1275.2.d.d	$1275$	$2$	1275.d	85.c	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}+q^{4}+iq^{6}+4q^{7}+3iq^{8}+\cdots\)
1275.2.d.e	$1275$	$2$	1275.d	85.c	$2$	$4$	$4$	$10.181$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
1275.2.d.f	$1275$	$2$	1275.d	85.c	$2$	$4$	$4$	$10.181$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-2+\beta _{3})q^{4}+\beta _{1}q^{6}+\cdots\)
1275.2.d.g	$1275$	$2$	1275.d	85.c	$2$	$8$	$8$	$10.181$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(-8\)	\(0\)	\(4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1275.2.d.h	$1275$	$2$	1275.d	85.c	$2$	$8$	$8$	$10.181$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(-4\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
1275.2.d.i	$1275$	$2$	1275.d	85.c	$2$	$12$	$12$	$10.181$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-q^{3}+(-1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1275.2.d.j	$1275$	$2$	1275.d	85.c	$2$	$12$	$12$	$10.181$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+q^{3}+(-1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1275, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1275, [\chi]) \cong \)