Space of modular forms of level 58, weight 3, and Character 58.f

• Label: 58.3.f
• Level: $58$
• Weight: $3$
• Character orbit: 58.f
• Rep. character: $\chi_{58}(3,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $22$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	58.f (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(22\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(58, [\chi])\).

	Total	New	Old
Modular forms	204	60	144
Cusp forms	156	60	96
Eisenstein series	48	0	48

Trace form

60 * q + 2 * q^2 - 4 * q^8 + 24 * q^11 - 16 * q^14 - 28 * q^15 + 40 * q^16 + 46 * q^17 - 30 * q^18 - 28 * q^19 - 40 * q^20 - 432 * q^21 - 168 * q^22 - 116 * q^23 - 80 * q^24 - 58 * q^25 - 66 * q^26 - 216 * q^27 + 176 * q^29 + 144 * q^30 + 152 * q^31 - 8 * q^32 + 420 * q^33 + 210 * q^34 + 392 * q^35 + 220 * q^36 + 86 * q^37 + 280 * q^38 + 572 * q^39 + 84 * q^40 + 86 * q^41 - 248 * q^43 - 48 * q^44 - 244 * q^45 - 56 * q^46 - 128 * q^47 - 326 * q^49 - 110 * q^50 - 336 * q^51 - 56 * q^52 - 212 * q^53 + 152 * q^54 - 428 * q^55 + 32 * q^56 + 118 * q^58 - 8 * q^59 - 56 * q^60 + 250 * q^61 + 672 * q^63 + 416 * q^65 - 144 * q^66 + 560 * q^67 - 92 * q^68 + 800 * q^69 - 280 * q^70 - 868 * q^71 - 60 * q^72 - 70 * q^73 - 548 * q^74 - 1520 * q^75 - 504 * q^76 - 1188 * q^77 - 1048 * q^78 - 576 * q^79 - 918 * q^81 + 68 * q^82 + 176 * q^83 - 88 * q^84 - 680 * q^85 + 404 * q^87 + 298 * q^89 + 160 * q^90 + 840 * q^91 + 504 * q^92 + 784 * q^93 + 256 * q^94 + 1600 * q^95 + 372 * q^97 + 1150 * q^98 + 720 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(58, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
58.3.f.a	$58$	$3$	58.f	29.f	$28$	$24$	$2$	$1.580$		None		✓			58.3.f.a	$2$	$0$	\(-4\)	\(-4\)	\(28\)	\(34\)		$\mathrm{SU}(2)[C_{28}]$
58.3.f.b	$58$	$3$	58.f	29.f	$28$	$36$	$3$	$1.580$		None		✓	✓		58.3.f.b	$2$	$0$	\(6\)	\(4\)	\(-28\)	\(-34\)		$\mathrm{SU}(2)[C_{28}]$

Decomposition of \(S_{3}^{\mathrm{old}}(58, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(58, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 2}\)