Space of modular forms of level 156, weight 2, and Character 156.h

• Label: 156.2.h
• Level: $156$
• Weight: $2$
• Character orbit: 156.h
• Rep. character: $\chi_{156}(155,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 156 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(56\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(156, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

24 * q - 4 * q^4 - 4 * q^9 - 8 * q^10 - 2 * q^12 - 8 * q^13 - 8 * q^16 + 20 * q^22 - 18 * q^30 - 22 * q^36 - 34 * q^42 + 46 * q^48 - 32 * q^49 + 20 * q^52 - 16 * q^61 - 4 * q^64 + 32 * q^66 + 34 * q^78 + 12 * q^81 + 20 * q^82 + 60 * q^88 - 10 * q^90 + 80 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(156, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.2.h.a	$156$	$2$	156.h	156.h	$2$	$8$	$8$	$1.246$	8.0.592240896.6	\(\Q(\sqrt{-39}) \)		✓			156.2.h.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{5}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{2}q^{2}-\beta _{3}q^{3}-\beta _{4}q^{4}+(-\beta _{6}-\beta _{7})q^{5}+\cdots\)
156.2.h.b	$156$	$2$	156.h	156.h	$2$	$16$	$16$	$1.246$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓		156.2.h.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{2}+\beta _{6}q^{3}-\beta _{12}q^{4}-\beta _{4}q^{5}+\cdots\)