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

• Label: 116.2.i
• Level: $116$
• Weight: $2$
• Character orbit: 116.i
• Rep. character: $\chi_{116}(5,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $30$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 116 = 2^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	116.i (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(30\)
Trace bound:			\(3\)
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	12	96
Cusp forms	72	12	60
Eisenstein series	36	0	36

Trace form

12 * q - 2 * q^5 + 4 * q^7 + 8 * q^9 + 4 * q^13 - 14 * q^15 - 28 * q^21 + 2 * q^23 - 20 * q^25 - 12 * q^29 - 14 * q^31 + 14 * q^33 - 38 * q^35 + 14 * q^37 - 14 * q^39 + 14 * q^43 + 8 * q^45 + 28 * q^47 - 8 * q^49 + 14 * q^51 + 18 * q^53 + 28 * q^55 + 28 * q^57 + 56 * q^61 - 2 * q^63 + 32 * q^65 + 50 * q^67 - 28 * q^69 + 30 * q^71 - 28 * q^77 - 14 * q^79 - 4 * q^81 - 60 * q^83 - 14 * q^85 - 14 * q^87 - 70 * q^89 + 20 * q^91 - 42 * q^93 - 70 * q^97

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.i.a	$116$	$2$	116.i	29.e	$14$	$6$	$1$	$0.926$	\(\Q(\zeta_{14})\)	None		✓			116.2.i.a	$2$	$0$	\(0\)	\(-7\)	\(-1\)	\(9\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(-1-\zeta_{14}^{3})q^{3}+(-1-\zeta_{14}^{2}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
116.2.i.b	$116$	$2$	116.i	29.e	$14$	$6$	$1$	$0.926$	\(\Q(\zeta_{14})\)	None		✓			116.2.i.b	$2$	$0$	\(0\)	\(7\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q+(1+\zeta_{14}^{3})q^{3}+(1-2\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots\)

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

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