Space of modular forms of level 1058 and weight 6

• Label: 1058.6
• Level: 1058
• Weight: 6
• Dimension: 57970
• Nonzero newspaces: 4
• Sturm bound: 418968
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(418968\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(1058))\).

	Total	New	Old
Modular forms	175318	57970	117348
Cusp forms	173822	57970	115852
Eisenstein series	1496	0	1496

Trace form

57970 * q - 18524 * q^15 + 15884 * q^17 + 24992 * q^18 + 3124 * q^19 - 7744 * q^20 - 50028 * q^21 - 21296 * q^22 - 20284 * q^23 - 2728 * q^25 + 13904 * q^26 + 88572 * q^27 + 41536 * q^28 + 44924 * q^29 + 67232 * q^30 + 484 * q^31 - 165044 * q^33 - 31900 * q^35 + 144232 * q^37 + 122760 * q^39 + 1364 * q^41 - 118712 * q^43 - 267300 * q^45 - 146168 * q^47 - 40260 * q^49 + 141768 * q^51 + 143924 * q^53 - 421520 * q^54 - 19888 * q^55 + 14080 * q^56 + 425964 * q^57 + 355168 * q^58 + 438900 * q^59 + 168256 * q^60 + 500720 * q^61 + 205392 * q^62 + 28820 * q^63 - 785708 * q^65 - 630080 * q^66 - 377432 * q^67 - 406912 * q^68 - 501050 * q^69 - 717376 * q^70 - 705100 * q^71 - 174592 * q^72 - 42152 * q^73 + 214720 * q^74 + 327008 * q^75 + 1368620 * q^77 + 965712 * q^78 + 1686564 * q^79 + 326656 * q^80 + 1727352 * q^81 + 270688 * q^82 + 21296 * q^83 - 355520 * q^84 - 1471492 * q^85 - 1266320 * q^86 - 481668 * q^87 - 302236 * q^89 - 728728 * q^91 - 2019732 * q^95 - 1175768 * q^97 + 10912 * q^98 + 2082432 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(1058))\)

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
1058.6.a	\(\chi_{1058}(1, \cdot)\)	1058.6.a.a	1	1
		1058.6.a.b	1
		1058.6.a.c	2
		1058.6.a.d	2
		1058.6.a.e	3
		1058.6.a.f	3
		1058.6.a.g	3
		1058.6.a.h	3
		1058.6.a.i	4
		1058.6.a.j	4
		1058.6.a.k	4
		1058.6.a.l	6
		1058.6.a.m	6
		1058.6.a.n	10
		1058.6.a.o	10
		1058.6.a.p	12
		1058.6.a.q	16
		1058.6.a.r	20
		1058.6.a.s	25
		1058.6.a.t	25
		1058.6.a.u	25
		1058.6.a.v	25
1058.6.c	\(\chi_{1058}(177, \cdot)\)	n/a	2100	10
1058.6.e	\(\chi_{1058}(47, \cdot)\)	n/a	5060	22
1058.6.g	\(\chi_{1058}(3, \cdot)\)	n/a	50600	220

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(1058))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(1058)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)