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

• Label: 475.2.p
• Level: $475$
• Weight: $2$
• Character orbit: 475.p
• Rep. character: $\chi_{475}(107,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $112$
• Newform subspaces: $9$
• Sturm bound: $100$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 95 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(100\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

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

	Total	New	Old
Modular forms	224	128	96
Cusp forms	176	112	64
Eisenstein series	48	16	32

Trace form

\( 112 q + 6 q^{2} + 6 q^{3} + 4 q^{6} + 12 q^{7} + O(q^{10}) \)

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.p.a	$475$	$2$	475.p	95.l	$12$	$4$	$1$	$3.793$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(-2\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{12}+\zeta_{12}^{2})q^{2}+(2+2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.b	$475$	$2$	475.p	95.l	$12$	$4$	$1$	$3.793$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(6\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}+\zeta_{12}^{2}-2\zeta_{12}^{3})q^{3}+(2\zeta_{12}+\cdots)q^{4}+\cdots\)
475.2.p.c	$475$	$2$	475.p	95.l	$12$	$4$	$1$	$3.793$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(2\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}-\zeta_{12}^{2})q^{2}+(-2-2\zeta_{12}+\cdots)q^{3}+\cdots\)
475.2.p.d	$475$	$2$	475.p	95.l	$12$	$4$	$1$	$3.793$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(6\)	\(6\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{12}+\zeta_{12}^{2}+2\zeta_{12}^{3})q^{2}+(1+\cdots)q^{3}+\cdots\)
475.2.p.e	$475$	$2$	475.p	95.l	$12$	$16$	$4$	$3.793$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+\beta _{14}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{6}q^{6}+\cdots\)
475.2.p.f	$475$	$2$	475.p	95.l	$12$	$16$	$4$	$3.793$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{3}-\beta _{11})q^{2}+(-\beta _{6}+\beta _{14})q^{3}+\cdots\)
475.2.p.g	$475$	$2$	475.p	95.l	$12$	$16$	$4$	$3.793$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{11}+\beta _{15})q^{2}+(\beta _{5}+\beta _{7})q^{3}-3\beta _{13}q^{4}+\cdots\)
475.2.p.h	$475$	$2$	475.p	95.l	$12$	$24$	$6$	$3.793$		None		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$
475.2.p.i	$475$	$2$	475.p	95.l	$12$	$24$	$6$	$3.793$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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