Space of modular forms of level 2058 and weight 2

• Label: 2058.2
• Level: 2058
• Weight: 2
• Dimension: 27648
• Nonzero newspaces: 12
• Sturm bound: 460992
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 2058 = 2 \cdot 3 \cdot 7^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(460992\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2058))\).

	Total	New	Old
Modular forms	117432	27648	89784
Cusp forms	113065	27648	85417
Eisenstein series	4367	0	4367

Trace form

27648 * q - 2 * q^3 - 4 * q^4 - 12 * q^5 - 6 * q^6 - 8 * q^9 - 12 * q^10 - 24 * q^11 - 2 * q^12 - 16 * q^13 - 12 * q^17 + 12 * q^18 - 16 * q^19 - 12 * q^23 + 6 * q^24 - 24 * q^25 - 12 * q^26 - 2 * q^27 - 24 * q^29 - 12 * q^30 - 40 * q^31 - 24 * q^33 - 24 * q^34 - 8 * q^36 + 168 * q^37 + 132 * q^38 + 168 * q^39 + 156 * q^40 + 288 * q^41 + 84 * q^42 + 256 * q^43 + 144 * q^44 + 156 * q^45 + 456 * q^46 + 300 * q^47 + 26 * q^48 + 336 * q^49 + 288 * q^50 + 348 * q^51 + 64 * q^52 + 300 * q^53 + 18 * q^54 + 804 * q^55 + 84 * q^56 + 140 * q^57 + 348 * q^58 + 288 * q^59 + 96 * q^60 + 352 * q^61 + 144 * q^62 + 14 * q^63 - 4 * q^64 - 84 * q^65 - 24 * q^67 - 12 * q^68 - 24 * q^69 - 72 * q^71 - 12 * q^72 - 52 * q^73 - 36 * q^74 - 38 * q^75 - 16 * q^76 - 24 * q^78 - 120 * q^79 - 12 * q^80 + 112 * q^81 - 72 * q^82 + 216 * q^83 + 144 * q^85 - 60 * q^86 + 276 * q^87 - 12 * q^88 + 240 * q^89 - 12 * q^90 + 168 * q^91 - 24 * q^92 + 476 * q^93 - 72 * q^94 + 564 * q^95 + 6 * q^96 + 236 * q^97 + 336 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2058))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
2058.2.a	\(\chi_{2058}(1, \cdot)\)	2058.2.a.a	3	1
		2058.2.a.b	3
		2058.2.a.c	3
		2058.2.a.d	3
		2058.2.a.e	3
		2058.2.a.f	3
		2058.2.a.g	3
		2058.2.a.h	3
		2058.2.a.i	3
		2058.2.a.j	3
		2058.2.a.k	3
		2058.2.a.l	3
		2058.2.a.m	6
		2058.2.a.n	6
2058.2.d	\(\chi_{2058}(2057, \cdot)\)	2058.2.d.a	48	1
		2058.2.d.b	48
2058.2.e	\(\chi_{2058}(361, \cdot)\)	2058.2.e.a	6	2
		2058.2.e.b	6
		2058.2.e.c	6
		2058.2.e.d	6
		2058.2.e.e	6
		2058.2.e.f	6
		2058.2.e.g	6
		2058.2.e.h	6
		2058.2.e.i	6
		2058.2.e.j	6
		2058.2.e.k	6
		2058.2.e.l	6
		2058.2.e.m	12
		2058.2.e.n	12
2058.2.f	\(\chi_{2058}(1391, \cdot)\)	n/a	192	2
2058.2.i	\(\chi_{2058}(295, \cdot)\)	n/a	288	6
2058.2.j	\(\chi_{2058}(293, \cdot)\)	n/a	552	6
2058.2.m	\(\chi_{2058}(67, \cdot)\)	n/a	552	12
2058.2.p	\(\chi_{2058}(215, \cdot)\)	n/a	1128	12
2058.2.q	\(\chi_{2058}(43, \cdot)\)	n/a	2688	42
2058.2.s	\(\chi_{2058}(41, \cdot)\)	n/a	5544	42
2058.2.u	\(\chi_{2058}(25, \cdot)\)	n/a	5544	84
2058.2.x	\(\chi_{2058}(5, \cdot)\)	n/a	10920	84

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2058))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2058)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(686))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1029))\)\(^{\oplus 2}\)