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

• Label: 12.15.c
• Level: $12$
• Weight: $15$
• Character orbit: 12.c
• Rep. character: $\chi_{12}(5,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 12 = 2^{2} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	12.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	31	5	26
Cusp forms	25	5	20
Eisenstein series	6	0	6

Trace form

\( 5 q - 39 q^{3} + 320266 q^{7} - 953955 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(12, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
12.15.c.a	$12$	$15$	12.c	3.b	$2$	$1$	$1$	$14.919$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(-2187\)	\(0\)	\(-1389022\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-3^{7}q^{3}-1389022q^{7}+3^{14}q^{9}+\cdots\)
12.15.c.b	$12$	$15$	12.c	3.b	$2$	$4$	$4$	$14.919$	\(\mathbb{Q}[x]/(x^{4} + \cdots)\)	None		$2$	$0$	\(0\)	\(2148\)	\(0\)	\(1709288\)	$2^{14}\cdot 3^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(537-\beta _{1})q^{3}+(\beta _{1}+\beta _{2})q^{5}+(427322+\cdots)q^{7}+\cdots\)

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

\( S_{15}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{15}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)