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

• Label: 116.2.g
• Level: $116$
• Weight: $2$
• Character orbit: 116.g
• Rep. character: $\chi_{116}(25,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.g (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	108	18	90
Cusp forms	72	18	54
Eisenstein series	36	0	36

Trace form

18 * q - 4 * q^5 - 4 * q^7 - 5 * q^9 + 4 * q^11 - 18 * q^13 + 24 * q^15 + 2 * q^17 + 6 * q^19 + 8 * q^21 - 20 * q^23 - 7 * q^25 - 24 * q^27 - 11 * q^29 - 22 * q^31 - 36 * q^33 + 22 * q^35 - 30 * q^37 - 32 * q^39 + 6 * q^41 - 18 * q^43 + 25 * q^45 + 12 * q^47 + 43 * q^49 + 22 * q^51 + 27 * q^53 + 66 * q^55 + 28 * q^57 + 60 * q^59 - 22 * q^61 + 62 * q^63 + 19 * q^65 + 10 * q^67 + 64 * q^69 - 40 * q^71 + 13 * q^73 - 60 * q^75 - 2 * q^77 - 18 * q^79 - 97 * q^81 - 28 * q^83 - 54 * q^85 - 28 * q^87 - 2 * q^89 - 60 * q^91 + 6 * q^93 - 124 * q^95 + 31 * q^97 + 4 * q^99

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.g.a	$116$	$2$	116.g	29.d	$7$	$6$	$1$	$0.926$	\(\Q(\zeta_{14})\)	None		✓			116.2.g.a	$2$	$0$	\(0\)	\(3\)	\(-3\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-1+2\zeta_{14}-2\zeta_{14}^{2}+2\zeta_{14}^{3}+\cdots)q^{3}+\cdots\)
116.2.g.b	$116$	$2$	116.g	29.d	$7$	$12$	$2$	$0.926$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		116.2.g.b	$2$	$0$	\(0\)	\(-3\)	\(-1\)	\(-7\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+(-\beta _{1}-\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)

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

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