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

• Label: 290.2.c
• Level: $290$
• Weight: $2$
• Character orbit: 290.c
• Rep. character: $\chi_{290}(231,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	50	10	40
Cusp forms	42	10	32
Eisenstein series	8	0	8

Trace form

10 * q - 10 * q^4 - 2 * q^5 + 4 * q^6 - 14 * q^9 - 4 * q^13 + 10 * q^16 + 2 * q^20 - 12 * q^22 + 8 * q^23 - 4 * q^24 + 10 * q^25 + 2 * q^29 + 8 * q^30 - 24 * q^33 - 8 * q^34 + 4 * q^35 + 14 * q^36 - 12 * q^38 - 16 * q^42 + 10 * q^45 + 22 * q^49 + 40 * q^51 + 4 * q^52 + 4 * q^53 + 32 * q^54 - 80 * q^57 + 28 * q^58 - 60 * q^59 + 20 * q^62 + 24 * q^63 - 10 * q^64 + 16 * q^65 - 16 * q^67 + 56 * q^71 - 12 * q^74 - 32 * q^78 - 2 * q^80 + 42 * q^81 - 8 * q^82 - 12 * q^86 - 8 * q^87 + 12 * q^88 + 16 * q^91 - 8 * q^92 - 24 * q^93 - 8 * q^94 + 4 * 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.c.a	$290$	$2$	290.c	29.b	$2$	$2$	$2$	$2.316$	\(\Q(\sqrt{-1}) \)	None		✓			290.2.c.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+i q^{2}-q^{4}-q^{5}+4 q^{7}-i q^{8}+\cdots\)
290.2.c.b	$290$	$2$	290.c	29.b	$2$	$4$	$4$	$2.316$	\(\Q(i, \sqrt{29})\)	None		✓			290.2.c.b	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
290.2.c.c	$290$	$2$	290.c	29.b	$2$	$4$	$4$	$2.316$	\(\Q(i, \sqrt{5})\)	None		✓			290.2.c.c	$2$	$0$	\(0\)	\(0\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3})q^{3}-q^{4}+q^{5}+\cdots\)

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

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