Space of modular forms of level 296, weight 2, and Character 296.i

• Label: 296.2.i
• Level: $296$
• Weight: $2$
• Character orbit: 296.i
• Rep. character: $\chi_{296}(121,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $3$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 296 = 2^{3} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	296.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(76\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(296, [\chi])\).

	Total	New	Old
Modular forms	84	18	66
Cusp forms	68	18	50
Eisenstein series	16	0	16

Trace form

18 * q - 2 * q^3 + q^5 + 2 * q^7 - 7 * q^9 + 16 * q^11 + 4 * q^13 + 6 * q^15 + q^17 - 6 * q^19 + 6 * q^21 - 12 * q^25 + 52 * q^27 + 2 * q^29 - 32 * q^31 + 4 * q^33 - 6 * q^35 - 7 * q^37 + 10 * q^39 - 3 * q^41 - 8 * q^43 - 54 * q^45 + 8 * q^47 - 19 * q^49 + 12 * q^51 + 20 * q^53 + 4 * q^55 - 22 * q^57 - 2 * q^59 + q^61 - 72 * q^63 + 12 * q^65 - 6 * q^67 - 12 * q^69 - 10 * q^71 - 20 * q^73 + 8 * q^75 - 4 * q^77 + 14 * q^79 - 17 * q^81 - 26 * q^83 + 2 * q^85 - 28 * q^87 + 21 * q^89 - 14 * q^91 + 36 * q^93 - 6 * q^95 - 6 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(296, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
296.2.i.a	$296$	$2$	296.i	37.c	$3$	$2$	$1$	$2.364$	\(\Q(\sqrt{-3}) \)	None		✓			296.2.i.a	$2$	$0$	\(0\)	\(1\)	\(-3\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{3}-3\zeta_{6}q^{5}-3\zeta_{6}q^{7}+(2-2\zeta_{6})q^{9}+\cdots\)
296.2.i.b	$296$	$2$	296.i	37.c	$3$	$6$	$3$	$2.364$	6.0.591408.1	None		✓			296.2.i.b	$2$	$0$	\(0\)	\(-2\)	\(1\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
296.2.i.c	$296$	$2$	296.i	37.c	$3$	$10$	$5$	$2.364$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		296.2.i.c	$2$	$0$	\(0\)	\(-1\)	\(3\)	\(3\)	$2^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{9}q^{3}+(\beta _{2}+\beta _{6}+\beta _{9})q^{5}+(1-\beta _{7}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(296, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(296, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(148, [\chi])\)\(^{\oplus 2}\)