Space of modular forms of level 15, weight 12, and Character 15.b

• Label: 15.12.b
• Level: $15$
• Weight: $12$
• Character orbit: 15.b
• Rep. character: $\chi_{15}(4,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	15.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(15, [\chi])\).

	Total	New	Old
Modular forms	24	12	12
Cusp forms	20	12	8
Eisenstein series	4	0	4

Trace form

\( 12 q - 16314 q^{4} + 2556 q^{5} + 4374 q^{6} - 708588 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(15, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.12.b.a	$15$	$12$	15.b	5.b	$2$	$12$	$12$	$11.525$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2556\)	\(0\)	$2^{10}\cdot 3^{28}\cdot 5^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}-\beta _{4}q^{3}+(-1359+\beta _{1})q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(15, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(15, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)