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

• Label: 290.2.e
• Level: $290$
• Weight: $2$
• Character orbit: 290.e
• Rep. character: $\chi_{290}(17,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $30$
• Newform subspaces: $6$
• Sturm bound: $90$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(90\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	98	30	68
Cusp forms	82	30	52
Eisenstein series	16	0	16

Trace form

30 * q + 2 * q^2 + 30 * q^4 + 2 * q^8 - 38 * q^9 + 8 * q^11 - 18 * q^13 - 4 * q^14 - 16 * q^15 + 30 * q^16 - 24 * q^17 - 10 * q^18 - 16 * q^21 - 2 * q^25 - 10 * q^26 - 16 * q^31 + 2 * q^32 - 4 * q^33 + 16 * q^34 + 16 * q^35 - 38 * q^36 + 28 * q^38 + 24 * q^39 - 2 * q^41 + 8 * q^42 + 8 * q^44 + 40 * q^45 + 4 * q^46 - 18 * q^50 - 18 * q^52 - 18 * q^53 + 16 * q^55 - 4 * q^56 + 48 * q^57 - 12 * q^58 - 16 * q^60 - 22 * q^61 - 24 * q^63 + 30 * q^64 + 26 * q^65 + 24 * q^66 - 16 * q^67 - 24 * q^68 + 8 * q^69 - 12 * q^70 - 10 * q^72 + 28 * q^73 - 44 * q^75 - 40 * q^77 + 12 * q^78 - 16 * q^79 + 46 * q^81 + 34 * q^82 + 56 * q^83 - 16 * q^84 - 36 * q^85 - 56 * q^87 + 30 * q^89 - 44 * q^90 + 52 * q^93 - 48 * q^95 - 24 * 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.e.a	$290$	$2$	290.e	145.j	$4$	$2$	$1$	$2.316$	\(\Q(\sqrt{-1}) \)	None		✓			290.2.e.a	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+2 i q^{3}+q^{4}+(2 i+1)q^{5}+\cdots\)
290.2.e.b	$290$	$2$	290.e	145.j	$4$	$2$	$1$	$2.316$	\(\Q(\sqrt{-1}) \)	None		✓			290.2.e.b	$2$	$0$	\(2\)	\(0\)	\(2\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}+2 i q^{3}+q^{4}+(-2 i+1)q^{5}+\cdots\)
290.2.e.c	$290$	$2$	290.e	145.j	$4$	$2$	$1$	$2.316$	\(\Q(\sqrt{-1}) \)	None		✓			290.2.e.c	$2$	$0$	\(2\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}+q^{4}+(i+2)q^{5}+(2 i-2)q^{7}+\cdots\)
290.2.e.d	$290$	$2$	290.e	145.j	$4$	$4$	$2$	$2.316$	\(\Q(i, \sqrt{19})\)	None		✓			290.2.e.d	$2$	$0$	\(-4\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{3}q^{5}+\beta _{2}q^{6}+\cdots\)
290.2.e.e	$290$	$2$	290.e	145.j	$4$	$8$	$4$	$2.316$	8.0.6420496384.3	None		✓			290.2.e.e	$2$	$0$	\(-8\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}+\beta _{1}q^{3}+q^{4}+(-2\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
290.2.e.f	$290$	$2$	290.e	145.j	$4$	$12$	$6$	$2.316$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		290.2.e.f	$2$	$0$	\(12\)	\(0\)	\(-6\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{3}+\cdots\)

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

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