Space of modular forms of level 475, weight 2, and Character 475.b

• Label: 475.2.b
• Level: $475$
• Weight: $2$
• Character orbit: 475.b
• Rep. character: $\chi_{475}(324,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $5$
• Sturm bound: $100$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(100\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

	Total	New	Old
Modular forms	56	28	28
Cusp forms	44	28	16
Eisenstein series	12	0	12

Trace form

\( 28 q - 30 q^{4} - 4 q^{6} - 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
475.2.b.a	$475$	$2$	475.b	5.b	$2$	$2$	$2$	$3.793$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{3}+2q^{4}-iq^{7}-q^{9}+3q^{11}+\cdots\)
475.2.b.b	$475$	$2$	475.b	5.b	$2$	$6$	$6$	$3.793$	6.0.1827904.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{4}+\beta _{5})q^{2}+(\beta _{1}+\beta _{4})q^{3}+(-1+\cdots)q^{4}+\cdots\)
475.2.b.c	$475$	$2$	475.b	5.b	$2$	$6$	$6$	$3.793$	6.0.153664.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(-3+\cdots)q^{4}+\cdots\)
475.2.b.d	$475$	$2$	475.b	5.b	$2$	$6$	$6$	$3.793$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}+(\beta _{2}-\beta _{4})q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{6}+\cdots\)
475.2.b.e	$475$	$2$	475.b	5.b	$2$	$8$	$8$	$3.793$	8.0.2058981376.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{6}q^{2}+\beta _{1}q^{3}+(-2-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)