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

• Label: 58.2.d
• Level: $58$
• Weight: $2$
• Character orbit: 58.d
• Rep. character: $\chi_{58}(7,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	58.d (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	54	18	36
Cusp forms	30	18	12
Eisenstein series	24	0	24

Trace form

18 * q - q^2 - 3 * q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 - q^8 - 17 * q^9 - 10 * q^10 - 8 * q^11 + 12 * q^13 - 8 * q^14 - 18 * q^15 - 3 * q^16 - 22 * q^17 - 5 * q^18 - 12 * q^19 + 3 * q^20 + 2 * q^21 + 4 * q^22 + 28 * q^23 + 8 * q^24 + 11 * q^25 + 11 * q^26 + 48 * q^27 - 4 * q^28 + q^29 + 56 * q^30 - 4 * q^31 - q^32 + 30 * q^33 + 5 * q^34 + 4 * q^35 - 3 * q^36 + 18 * q^37 - 14 * q^38 - 20 * q^39 + 11 * q^40 - 42 * q^41 - 28 * q^42 - 12 * q^43 + 20 * q^44 - 23 * q^45 - 28 * q^46 - 30 * q^47 + 19 * q^49 + 5 * q^50 - 20 * q^51 - 16 * q^52 - 9 * q^53 - 12 * q^54 + 12 * q^55 - 8 * q^56 - 20 * q^57 - 15 * q^58 - 18 * q^60 + 26 * q^61 - 26 * q^62 + 2 * q^63 - 3 * q^64 - 11 * q^65 - 48 * q^66 + 4 * q^67 - 8 * q^68 - 8 * q^69 - 12 * q^70 + 26 * q^71 - 5 * q^72 - 17 * q^73 + 44 * q^74 + 24 * q^75 + 16 * q^76 + 22 * q^77 + 60 * q^78 - 60 * q^79 - 4 * q^80 + 65 * q^81 + 10 * q^82 - 4 * q^83 + 44 * q^84 + 12 * q^85 + 44 * q^86 + 20 * q^87 + 4 * q^88 + 52 * q^89 - 24 * q^90 + 60 * q^91 + 28 * q^92 - 66 * q^93 + 20 * q^94 + 80 * q^95 - 6 * q^96 + q^97 + 55 * q^98 + 40 * q^99

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.d.a	$58$	$2$	58.d	29.d	$7$	$6$	$1$	$0.463$	\(\Q(\zeta_{14})\)	None		✓			58.2.d.a	$2$	$0$	\(1\)	\(3\)	\(-4\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q-\zeta_{14}^{4}q^{2}+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+\cdots\)
58.2.d.b	$58$	$2$	58.d	29.d	$7$	$12$	$2$	$0.463$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		58.2.d.b	$2$	$0$	\(-2\)	\(-3\)	\(0\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{7}]$	\(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{6}q^{4}+(\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)

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

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