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

• Label: 475.2.bb
• Level: $475$
• Weight: $2$
• Character orbit: 475.bb
• Rep. character: $\chi_{475}(32,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $336$
• Newform subspaces: $3$
• Sturm bound: $100$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bb (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(100\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	672	384	288
Cusp forms	528	336	192
Eisenstein series	144	48	96

Trace form

\( 336 q + 12 q^{2} + 12 q^{3} - 48 q^{6} + 18 q^{8} + O(q^{10}) \)

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.bb.a	$475$	$2$	475.bb	95.r	$36$	$72$	$6$	$3.793$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
475.2.bb.b	$475$	$2$	475.bb	95.r	$36$	$96$	$8$	$3.793$		None		$4$	$0$	\(12\)	\(12\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$
475.2.bb.c	$475$	$2$	475.bb	95.r	$36$	$168$	$14$	$3.793$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{36}]$

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

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