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

• Label: 156.2.w
• Level: $156$
• Weight: $2$
• Character orbit: 156.w
• Rep. character: $\chi_{156}(7,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $56$
• Newform subspaces: $4$
• Sturm bound: $56$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(56\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	128	56	72
Cusp forms	96	56	40
Eisenstein series	32	0	32

Trace form

56 * q - 4 * q^5 + 28 * q^9 - 32 * q^14 - 8 * q^16 - 52 * q^20 + 8 * q^21 - 12 * q^22 + 12 * q^24 - 40 * q^26 - 28 * q^28 - 80 * q^32 - 24 * q^34 - 12 * q^37 + 56 * q^40 - 56 * q^41 + 12 * q^42 + 56 * q^44 - 8 * q^45 + 36 * q^46 + 16 * q^48 - 72 * q^49 + 52 * q^50 + 16 * q^52 - 24 * q^53 + 108 * q^56 - 48 * q^57 + 56 * q^58 + 16 * q^60 - 20 * q^61 + 60 * q^62 - 24 * q^65 + 16 * q^66 - 24 * q^68 - 16 * q^70 - 76 * q^73 + 24 * q^74 - 12 * q^76 + 4 * q^78 - 4 * q^80 - 28 * q^81 - 60 * q^82 + 4 * q^85 - 12 * q^88 + 100 * q^89 + 120 * q^92 - 8 * q^93 + 28 * q^94 - 40 * q^96 + 36 * q^97 + 148 * q^98

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.w.a	$156$	$2$	156.w	52.l	$12$	$4$	$1$	$1.246$	\(\Q(\zeta_{12})\)	None		✓			156.2.w.a	$2$	$0$	\(2\)	\(0\)	\(-4\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.b	$156$	$2$	156.w	52.l	$12$	$4$	$1$	$1.246$	\(\Q(\zeta_{12})\)	None		✓			156.2.w.a	$2$	$0$	\(4\)	\(0\)	\(-4\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
156.2.w.c	$156$	$2$	156.w	52.l	$12$	$24$	$6$	$1.246$		None		✓			156.2.w.c	$2$	$0$	\(-4\)	\(0\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$
156.2.w.d	$156$	$2$	156.w	52.l	$12$	$24$	$6$	$1.246$		None		✓			156.2.w.c	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)