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

• Label: 290.2.m
• Level: $290$
• Weight: $2$
• Character orbit: 290.m
• Rep. character: $\chi_{290}(51,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $60$
• 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.m (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
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	300	60	240
Cusp forms	252	60	192
Eisenstein series	48	0	48

Trace form

60 * q + 10 * q^4 + 2 * q^5 + 10 * q^6 + 14 * q^9 + 4 * q^13 - 10 * q^16 - 2 * q^20 - 14 * q^21 - 16 * q^22 + 48 * q^23 - 10 * q^24 - 10 * q^25 - 84 * q^27 - 30 * q^29 + 20 * q^30 - 28 * q^31 + 24 * q^33 + 8 * q^34 - 4 * q^35 - 28 * q^36 - 28 * q^37 - 16 * q^38 - 28 * q^39 + 16 * q^42 + 28 * q^44 - 10 * q^45 + 28 * q^47 - 36 * q^49 - 40 * q^51 - 4 * q^52 - 4 * q^53 + 52 * q^54 + 28 * q^55 + 136 * q^57 + 32 * q^59 - 56 * q^61 - 20 * q^62 + 60 * q^63 + 10 * q^64 + 12 * q^65 + 16 * q^67 + 28 * q^68 - 56 * q^73 - 16 * q^74 - 112 * q^77 - 80 * q^78 - 56 * q^79 + 2 * q^80 + 42 * q^81 + 8 * q^82 - 56 * q^83 - 84 * q^84 + 12 * q^86 - 132 * q^87 + 16 * q^88 - 28 * q^89 + 68 * q^91 - 48 * q^92 - 88 * q^93 - 6 * q^94 - 4 * q^96 - 56 * q^97 - 112 * q^98

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.m.a	$290$	$2$	290.m	29.e	$14$	$24$	$4$	$2.316$		None		✓			290.2.m.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-2\)		$\mathrm{SU}(2)[C_{14}]$
290.2.m.b	$290$	$2$	290.m	29.e	$14$	$36$	$6$	$2.316$		None		✓	✓		290.2.m.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(2\)		$\mathrm{SU}(2)[C_{14}]$

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

\( S_{2}^{\mathrm{old}}(290, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 2}\)