Space of modular forms of level 116, weight 2, and Character 116.c

• Label: 116.2.c
• Level: $116$
• Weight: $2$
• Character orbit: 116.c
• Rep. character: $\chi_{116}(57,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(116, [\chi])\).

	Total	New	Old
Modular forms	18	2	16
Cusp forms	12	2	10
Eisenstein series	6	0	6

Trace form

2 * q + 2 * q^5 - 4 * q^7 - 8 * q^9 + 10 * q^13 + 12 * q^23 - 8 * q^25 - 2 * q^29 - 14 * q^33 - 4 * q^35 - 8 * q^45 - 6 * q^49 + 28 * q^51 + 10 * q^53 + 28 * q^57 - 28 * q^59 + 16 * q^63 + 10 * q^65 - 8 * q^67 - 16 * q^71 - 10 * q^81 + 4 * q^83 - 28 * q^87 - 20 * q^91 + 14 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(116, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
116.2.c.a	$116$	$2$	116.c	29.b	$2$	$2$	$2$	$0.926$	\(\Q(\sqrt{-7}) \)	None		✓	✓	✓	116.2.c.a	$2$	$0$	\(0\)	\(0\)	\(2\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta q^{3}+q^{5}-2q^{7}-4q^{9}-\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)