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

• Label: 290.2.o
• Level: $290$
• Weight: $2$
• Character orbit: 290.o
• Rep. character: $\chi_{290}(3,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $180$
• Newform subspaces: $2$
• Sturm bound: $90$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.o (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(90\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	588	180	408
Cusp forms	492	180	312
Eisenstein series	96	0	96

Trace form

180 * q + 30 * q^4 - 38 * q^9 - 10 * q^10 - 8 * q^11 + 38 * q^13 - 4 * q^14 - 30 * q^16 - 40 * q^21 + 30 * q^25 - 60 * q^26 - 60 * q^27 - 40 * q^31 - 4 * q^33 + 16 * q^34 - 40 * q^35 + 10 * q^36 + 72 * q^37 + 28 * q^38 + 24 * q^39 + 10 * q^40 + 2 * q^41 + 8 * q^42 - 40 * q^43 - 48 * q^44 - 40 * q^45 - 4 * q^46 - 64 * q^47 + 84 * q^49 + 40 * q^50 + 18 * q^52 - 52 * q^53 + 32 * q^55 + 4 * q^56 + 48 * q^57 + 2 * q^58 - 28 * q^60 + 22 * q^61 - 136 * q^63 + 30 * q^64 - 26 * q^65 - 24 * q^66 - 16 * q^67 - 104 * q^69 - 32 * q^70 - 28 * q^73 + 112 * q^74 - 48 * q^75 - 84 * q^77 - 152 * q^78 - 16 * q^79 - 46 * q^81 - 34 * q^82 - 56 * q^83 - 16 * q^84 - 52 * q^85 + 76 * q^87 + 30 * q^89 - 178 * q^90 + 52 * q^93 - 84 * q^94 - 376 * q^95 + 8 * q^97 + 114 * q^98 + 32 * q^99

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.o.a	$290$	$2$	290.o	145.t	$28$	$84$	$7$	$2.316$		None		✓			290.2.o.a	$2$	$0$	\(0\)	\(4\)	\(14\)	\(12\)		$\mathrm{SU}(2)[C_{28}]$
290.2.o.b	$290$	$2$	290.o	145.t	$28$	$96$	$8$	$2.316$		None		✓	✓		290.2.o.b	$2$	$0$	\(0\)	\(-4\)	\(-14\)	\(-12\)		$\mathrm{SU}(2)[C_{28}]$

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

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