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

• Label: 1275.2.b
• Level: $1275$
• Weight: $2$
• Character orbit: 1275.b
• Rep. character: $\chi_{1275}(1174,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $11$
• Sturm bound: $360$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1275 = 3 \cdot 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1275.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(360\)
Trace bound:			\(11\)
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	48	144
Cusp forms	168	48	120
Eisenstein series	24	0	24

Trace form

\( 48 q - 48 q^{4} - 4 q^{6} - 48 q^{9} + O(q^{10}) \)

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.b.a	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-iq^{7}+\cdots\)
1275.2.b.b	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+2q^{4}-4iq^{7}-q^{9}-3q^{11}+\cdots\)
1275.2.b.c	$1275$	$2$	1275.b	5.b	$2$	$2$	$2$	$10.181$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{4}-iq^{7}-q^{9}+2q^{11}+\cdots\)
1275.2.b.d	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-3+\beta _{3})q^{4}+(1+\cdots)q^{6}+\cdots\)
1275.2.b.e	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{1}-\beta _{3})q^{2}-\beta _{3}q^{3}+3\beta _{2}q^{4}+(-1+\cdots)q^{6}+\cdots\)
1275.2.b.f	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-2+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
1275.2.b.g	$1275$	$2$	1275.b	5.b	$2$	$4$	$4$	$10.181$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{3}q^{6}+(-3\zeta_{8}+\cdots)q^{7}+\cdots\)
1275.2.b.h	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)
1275.2.b.i	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.3356224.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{6}+\cdots\)
1275.2.b.j	$1275$	$2$	1275.b	5.b	$2$	$6$	$6$	$10.181$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
1275.2.b.k	$1275$	$2$	1275.b	5.b	$2$	$8$	$8$	$10.181$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-\beta _{4}q^{3}+(-2-\beta _{1})q^{4}-\beta _{6}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1275, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(425, [\chi])\)\(^{\oplus 2}\)