Space of modular forms of level 290, weight 2, and Character 290.l

• Label: 290.2.l
• Level: $290$
• Weight: $2$
• Character orbit: 290.l
• Rep. character: $\chi_{290}(9,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.l (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(290, [\chi])\).

	Total	New	Old
Modular forms	288	96	192
Cusp forms	240	96	144
Eisenstein series	48	0	48

Trace form

96 * q - 16 * q^4 + 2 * q^5 - 6 * q^6 - 16 * q^9 - 14 * q^15 - 16 * q^16 - 5 * q^20 + 14 * q^21 - 6 * q^24 - 24 * q^25 + 42 * q^26 - 20 * q^29 - 36 * q^30 + 28 * q^31 - 66 * q^34 - 2 * q^36 - 28 * q^39 - 21 * q^40 + 28 * q^44 - 27 * q^45 + 54 * q^49 + 28 * q^50 + 48 * q^51 + 20 * q^54 - 56 * q^55 - 48 * q^59 + 14 * q^60 + 112 * q^61 - 16 * q^64 - 5 * q^65 + 56 * q^69 - 60 * q^71 + 88 * q^74 - 56 * q^76 + 2 * q^80 - 260 * q^81 - 84 * q^84 + 140 * q^85 - 124 * q^86 + 70 * q^90 - 212 * q^91 + 54 * q^94 + 224 * q^95 + 8 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(290, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
290.2.l.a	$290$	$2$	290.l	145.l	$14$	$48$	$8$	$2.316$		None		✓			290.2.l.a	$2$	$0$	\(-8\)	\(4\)	\(-6\)	\(-7\)		$\mathrm{SU}(2)[C_{14}]$
290.2.l.b	$290$	$2$	290.l	145.l	$14$	$48$	$8$	$2.316$		None		✓			290.2.l.a	$2$	$0$	\(8\)	\(-4\)	\(8\)	\(7\)		$\mathrm{SU}(2)[C_{14}]$

Decomposition of \(S_{2}^{\mathrm{old}}(290, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(290, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)