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

• Label: 475.2.j
• Level: $475$
• Weight: $2$
• Character orbit: 475.j
• Rep. character: $\chi_{475}(49,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $100$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.j (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 4 \)
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	112	64	48
Cusp forms	88	56	32
Eisenstein series	24	8	16

Trace form

\( 56 q + 24 q^{4} + 10 q^{6} + 26 q^{9} + O(q^{10}) \)

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.j.a	$475$	$2$	475.j	95.i	$6$	$4$	$2$	$3.793$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}-2\zeta_{12}^{2}q^{4}+2\zeta_{12}^{3}q^{7}+\cdots\)
475.2.j.b	$475$	$2$	475.j	95.i	$6$	$12$	$6$	$3.793$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}-\beta _{11}q^{3}+(2-\beta _{2}+3\beta _{3}+\cdots)q^{4}+\cdots\)
475.2.j.c	$475$	$2$	475.j	95.i	$6$	$16$	$8$	$3.793$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{14}q^{2}+(\beta _{7}+\beta _{13})q^{3}+(-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
475.2.j.d	$475$	$2$	475.j	95.i	$6$	$24$	$12$	$3.793$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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