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

• Label: 475.2.u
• Level: $475$
• Weight: $2$
• Character orbit: 475.u
• Rep. character: $\chi_{475}(24,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $168$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.u (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(100\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	336	192	144
Cusp forms	264	168	96
Eisenstein series	72	24	48

Trace form

\( 168 q + 24 q^{4} - 24 q^{6} + 12 q^{9} + O(q^{10}) \)

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.u.a	$475$	$2$	475.u	95.p	$18$	$12$	$2$	$3.793$	\(\Q(\zeta_{36})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{18}]$	\(q+(-\zeta_{36}^{5}+\zeta_{36}^{7}-\zeta_{36}^{9})q^{2}+(\zeta_{36}+\cdots)q^{3}+\cdots\)
475.2.u.b	$475$	$2$	475.u	95.p	$18$	$36$	$6$	$3.793$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
475.2.u.c	$475$	$2$	475.u	95.p	$18$	$36$	$6$	$3.793$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$
475.2.u.d	$475$	$2$	475.u	95.p	$18$	$84$	$14$	$3.793$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$

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

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