Space of modular forms of level 1058 and weight 4

• Label: 1058.4
• Level: 1058
• Weight: 4
• Dimension: 34782
• Nonzero newspaces: 4
• Sturm bound: 279312
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(279312\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1058))\).

	Total	New	Old
Modular forms	105490	34782	70708
Cusp forms	103994	34782	69212
Eisenstein series	1496	0	1496

Trace form

34782 * q - 1496 * q^15 - 352 * q^17 + 176 * q^18 + 440 * q^19 + 704 * q^20 + 2640 * q^21 + 968 * q^22 + 968 * q^23 + 1408 * q^25 + 440 * q^26 + 264 * q^27 - 352 * q^28 - 880 * q^29 - 2992 * q^30 - 2200 * q^31 - 3872 * q^33 - 2860 * q^35 - 2376 * q^37 + 264 * q^39 + 1100 * q^41 + 3432 * q^43 + 5940 * q^45 + 3784 * q^47 + 4356 * q^49 + 1320 * q^51 - 484 * q^53 - 6248 * q^54 - 13992 * q^55 - 3872 * q^56 - 16104 * q^57 - 3696 * q^58 - 9900 * q^59 - 176 * q^60 + 2112 * q^61 + 3432 * q^62 + 8360 * q^63 + 17248 * q^65 + 10912 * q^66 + 5808 * q^67 + 5984 * q^68 + 7480 * q^69 + 11616 * q^70 + 13640 * q^71 + 4928 * q^72 + 4224 * q^73 + 6688 * q^74 + 44 * q^75 - 880 * q^77 - 2904 * q^78 - 10252 * q^79 - 2816 * q^80 - 17160 * q^81 - 10032 * q^82 - 17908 * q^83 - 7568 * q^84 - 15796 * q^85 - 10472 * q^86 + 9372 * q^87 + 3740 * q^89 + 8008 * q^91 - 4752 * q^95 - 22660 * q^97 - 13904 * q^98 - 23100 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1058))\)

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
1058.4.a	\(\chi_{1058}(1, \cdot)\)	1058.4.a.a	1	1
		1058.4.a.b	1
		1058.4.a.c	1
		1058.4.a.d	1
		1058.4.a.e	2
		1058.4.a.f	2
		1058.4.a.g	2
		1058.4.a.h	2
		1058.4.a.i	2
		1058.4.a.j	2
		1058.4.a.k	3
		1058.4.a.l	3
		1058.4.a.m	3
		1058.4.a.n	3
		1058.4.a.o	4
		1058.4.a.p	6
		1058.4.a.q	8
		1058.4.a.r	8
		1058.4.a.s	12
		1058.4.a.t	15
		1058.4.a.u	15
		1058.4.a.v	15
		1058.4.a.w	15
1058.4.c	\(\chi_{1058}(177, \cdot)\)	n/a	1260	10
1058.4.e	\(\chi_{1058}(47, \cdot)\)	n/a	3036	22
1058.4.g	\(\chi_{1058}(3, \cdot)\)	n/a	30360	220

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1058))\) into lower level spaces

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