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

• Label: 156.2.b
• Level: $156$
• Weight: $2$
• Character orbit: 156.b
• Rep. character: $\chi_{156}(25,\cdot)$
• Character field: $\Q$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $56$
• Trace bound: $3$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	34	4	30
Cusp forms	22	4	18
Eisenstein series	12	0	12

Trace form

4 * q + 4 * q^9 + 4 * q^13 + 8 * q^17 - 16 * q^23 - 12 * q^25 - 8 * q^29 - 16 * q^35 + 8 * q^39 - 4 * q^49 - 16 * q^51 + 24 * q^53 + 24 * q^61 - 16 * q^65 - 16 * q^69 + 16 * q^75 + 48 * q^77 - 16 * q^79 + 4 * q^81 + 16 * q^87 + 16 * q^91 + 48 * q^95

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.b.a	$156$	$2$	156.b	13.b	$2$	$2$	$2$	$1.246$	\(\Q(\sqrt{-3}) \)	None		✓			156.2.b.a	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta q^{5}+q^{9}-\beta q^{11}+(-\beta-1)q^{13}+\cdots\)
156.2.b.b	$156$	$2$	156.b	13.b	$2$	$2$	$2$	$1.246$	\(\Q(\sqrt{-1}) \)	None		✓			156.2.b.b	$2$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+2\beta q^{7}+q^{9}-3\beta q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(156, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)