Space of modular forms of level 425, weight 4, and Character 425.b

• Label: 425.4.b
• Level: $425$
• Weight: $4$
• Character orbit: 425.b
• Rep. character: $\chi_{425}(324,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $11$
• Sturm bound: $180$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	425.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(180\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(425, [\chi])\).

	Total	New	Old
Modular forms	140	72	68
Cusp forms	128	72	56
Eisenstein series	12	0	12

Trace form

\( 72 q - 288 q^{4} - 8 q^{6} - 656 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(425, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
425.4.b.a	$425$	$4$	425.b	5.b	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{2}+7iq^{3}-q^{4}-21q^{6}-22iq^{7}+\cdots\)
425.4.b.b	$425$	$4$	425.b	5.b	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{2}+5iq^{3}-q^{4}-15q^{6}-22iq^{7}+\cdots\)
425.4.b.c	$425$	$4$	425.b	5.b	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{2}-8iq^{3}-q^{4}+24q^{6}+28iq^{7}+\cdots\)
425.4.b.d	$425$	$4$	425.b	5.b	$2$	$2$	$2$	$25.076$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3iq^{2}-10iq^{3}-q^{4}+30q^{6}-22iq^{7}+\cdots\)
425.4.b.e	$425$	$4$	425.b	5.b	$2$	$4$	$4$	$25.076$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2\zeta_{12}+\zeta_{12}^{2})q^{2}+(-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
425.4.b.f	$425$	$4$	425.b	5.b	$2$	$6$	$6$	$25.076$	6.0.27793984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}+2\beta _{4}-2\beta _{5})q^{3}+\cdots\)
425.4.b.g	$425$	$4$	425.b	5.b	$2$	$6$	$6$	$25.076$	6.0.27206656.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2\beta _{2}-\beta _{4})q^{2}+(\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
425.4.b.h	$425$	$4$	425.b	5.b	$2$	$6$	$6$	$25.076$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-4\beta _{3}-3\beta _{4}+\cdots)q^{3}+\cdots\)
425.4.b.i	$425$	$4$	425.b	5.b	$2$	$10$	$10$	$25.076$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(-6-\beta _{7}+2\beta _{9})q^{4}+\cdots\)
425.4.b.j	$425$	$4$	425.b	5.b	$2$	$12$	$12$	$25.076$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{7}-\beta _{8})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots\)
425.4.b.k	$425$	$4$	425.b	5.b	$2$	$20$	$20$	$25.076$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{11}-\beta _{13})q^{3}+(-6+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(425, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(425, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 2}\)