Space of modular forms of level 58, weight 2, and Character 58.e

• Label: 58.2.e
• Level: $58$
• Weight: $2$
• Character orbit: 58.e
• Rep. character: $\chi_{58}(5,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.e (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(58, [\chi])\).

	Total	New	Old
Modular forms	60	12	48
Cusp forms	36	12	24
Eisenstein series	24	0	24

Trace form

12 * q + 2 * q^4 - 2 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^9 - 26 * q^13 - 14 * q^15 - 2 * q^16 + 2 * q^20 + 14 * q^21 + 4 * q^22 - 16 * q^23 + 12 * q^24 + 22 * q^25 + 14 * q^26 - 4 * q^28 + 18 * q^29 + 16 * q^30 + 28 * q^31 - 10 * q^33 - 4 * q^34 + 4 * q^35 + 18 * q^36 - 28 * q^37 + 22 * q^38 + 28 * q^39 - 14 * q^40 - 4 * q^42 - 28 * q^43 - 28 * q^44 - 4 * q^45 - 14 * q^47 - 8 * q^49 - 28 * q^50 - 4 * q^51 - 2 * q^52 + 30 * q^53 - 32 * q^54 + 28 * q^55 - 20 * q^57 - 10 * q^58 - 48 * q^59 - 14 * q^60 - 28 * q^61 + 10 * q^62 + 22 * q^63 + 2 * q^64 + 2 * q^65 - 16 * q^67 - 14 * q^68 - 28 * q^69 + 30 * q^71 + 42 * q^73 + 2 * q^74 + 28 * q^76 + 14 * q^77 - 16 * q^78 + 28 * q^79 - 2 * q^80 + 26 * q^81 - 20 * q^82 + 28 * q^85 + 52 * q^86 + 4 * q^87 - 4 * q^88 + 14 * q^89 + 70 * q^90 - 4 * q^91 + 16 * q^92 + 66 * q^93 - 8 * q^94 + 2 * q^96 - 28 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(58, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
58.2.e.a	$58$	$2$	58.e	29.e	$14$	$12$	$2$	$0.463$	\(\Q(\zeta_{28})\)	None		✓	✓	✓	58.2.e.a	$2$	$0$	\(0\)	\(0\)	\(-2\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{14}]$	\(q-\zeta_{28}^{9}q^{2}+(-\zeta_{28}-\zeta_{28}^{3}-\zeta_{28}^{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(58, [\chi])\) into lower level spaces

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