Space of modular forms of level 49, weight 5, and Character 49.b

• Label: 49.5.b
• Level: $49$
• Weight: $5$
• Character orbit: 49.b
• Rep. character: $\chi_{49}(48,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $23$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	49.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(23\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(49, [\chi])\).

	Total	New	Old
Modular forms	22	16	6
Cusp forms	14	12	2
Eisenstein series	8	4	4

Trace form

\( 12 q - 4 q^{2} + 92 q^{4} - 68 q^{8} - 304 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(49, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
49.5.b.a	$49$	$5$	49.b	7.b	$2$	$4$	$4$	$5.065$	\(\Q(\sqrt{-3}, \sqrt{22})\)	None		$2$	$0$	\(8\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{1})q^{2}+\beta _{2}q^{3}+(10+4\beta _{1})q^{4}+\cdots\)
49.5.b.b	$49$	$5$	49.b	7.b	$2$	$8$	$8$	$5.065$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(-12\)	\(0\)	\(0\)	\(0\)	$7^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-2-\beta _{2})q^{2}-\beta _{3}q^{3}+(8+\beta _{1}+3\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(49, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(49, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)