Space of modular forms of level 156, weight 4, and Character 156.b

• Label: 156.4.b
• Level: $156$
• Weight: $4$
• Character orbit: 156.b
• Rep. character: $\chi_{156}(25,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $112$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(112\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(156, [\chi])\).

	Total	New	Old
Modular forms	90	6	84
Cusp forms	78	6	72
Eisenstein series	12	0	12

Trace form

6 * q - 6 * q^3 + 54 * q^9 - 34 * q^13 - 92 * q^17 + 136 * q^23 + 166 * q^25 - 54 * q^27 + 116 * q^29 - 56 * q^35 - 54 * q^39 - 632 * q^43 + 1042 * q^49 + 492 * q^51 - 1572 * q^53 + 960 * q^55 - 628 * q^61 - 536 * q^65 - 120 * q^69 + 426 * q^75 + 1776 * q^77 - 1568 * q^79 + 486 * q^81 - 276 * q^87 - 1736 * q^91 - 4968 * q^95

Decomposition of \(S_{4}^{\mathrm{new}}(156, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
156.4.b.a	$156$	$4$	156.b	13.b	$2$	$2$	$2$	$9.204$	\(\Q(\sqrt{-3}) \)	None		✓			156.4.b.a	$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3 q^{3}+2\beta q^{5}+3\beta q^{7}+9 q^{9}+\cdots\)
156.4.b.b	$156$	$4$	156.b	13.b	$2$	$4$	$4$	$9.204$	4.0.47664588.1	None		✓	✓		156.4.b.b	$2$	$0$	\(0\)	\(-12\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta _{1}q^{5}-\beta _{2}q^{7}+9q^{9}+(-3\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(156, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(156, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 2}\)