Space of modular forms of level 275, weight 2, and Character 275.b

• Label: 275.2.b
• Level: $275$
• Weight: $2$
• Character orbit: 275.b
• Rep. character: $\chi_{275}(199,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $5$
• Sturm bound: $60$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(60\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(275, [\chi])\).

	Total	New	Old
Modular forms	36	16	20
Cusp forms	24	16	8
Eisenstein series	12	0	12

Trace form

\( 16 q - 10 q^{4} - 16 q^{6} - 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(275, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
275.2.b.a	$275$	$2$	275.b	5.b	$2$	$2$	$2$	$2.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}+2iq^{7}+\cdots\)
275.2.b.b	$275$	$2$	275.b	5.b	$2$	$2$	$2$	$2.196$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+3iq^{8}+3q^{9}-q^{11}+\cdots\)
275.2.b.c	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	\(\Q(i, \sqrt{13})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}+(-2+\beta _{3})q^{4}+\cdots\)
275.2.b.d	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{2}+(\zeta_{8}-\zeta_{8}^{2})q^{3}+(-1-\zeta_{8}^{3})q^{4}+\cdots\)
275.2.b.e	$275$	$2$	275.b	5.b	$2$	$4$	$4$	$2.196$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(275, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(275, [\chi]) \cong \)