Space of modular forms of level 1058 and weight 2

• Label: 1058.2
• Level: 1058
• Weight: 2
• Dimension: 11595
• Nonzero newspaces: 4
• Sturm bound: 139656
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Sturm bound:			\(139656\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1058))\).

	Total	New	Old
Modular forms	35662	11595	24067
Cusp forms	34167	11595	22572
Eisenstein series	1495	0	1495

Trace form

11595 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 + 4 * q^12 + 14 * q^13 + 8 * q^14 - 20 * q^15 + q^16 - 26 * q^17 - 75 * q^18 - 24 * q^19 - 38 * q^20 - 100 * q^21 - 32 * q^22 - 44 * q^23 + 4 * q^24 - 57 * q^25 - 30 * q^26 - 92 * q^27 - 36 * q^28 - 14 * q^29 - 64 * q^30 - 12 * q^31 + q^32 + 4 * q^33 + 18 * q^34 + 4 * q^35 + 13 * q^36 - 50 * q^37 + 20 * q^38 - 32 * q^39 + 6 * q^40 - 2 * q^41 + 32 * q^42 - 44 * q^43 + 12 * q^44 - 54 * q^45 - 40 * q^47 + 4 * q^48 - 75 * q^49 + 31 * q^50 - 16 * q^51 + 14 * q^52 + 10 * q^53 - 4 * q^54 - 104 * q^55 - 36 * q^56 - 140 * q^57 - 58 * q^58 - 160 * q^59 - 20 * q^60 - 114 * q^61 - 100 * q^62 - 116 * q^63 + q^64 - 224 * q^65 - 128 * q^66 - 20 * q^67 - 70 * q^68 - 110 * q^69 - 128 * q^70 - 148 * q^71 - 75 * q^72 - 14 * q^73 - 138 * q^74 - 228 * q^75 + 20 * q^76 - 124 * q^77 - 76 * q^78 - 140 * q^79 - 38 * q^80 - 143 * q^81 - 46 * q^82 - 92 * q^83 - 12 * q^84 - 24 * q^85 - 12 * q^87 + 12 * q^88 + 46 * q^89 + 78 * q^90 + 24 * q^91 + 128 * q^93 + 48 * q^94 - 12 * q^95 + 4 * q^96 - 78 * q^97 - 31 * q^98 - 196 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1058))\)

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
1058.2.a	\(\chi_{1058}(1, \cdot)\)	1058.2.a.a	1	1
		1058.2.a.b	1
		1058.2.a.c	1
		1058.2.a.d	1
		1058.2.a.e	1
		1058.2.a.f	2
		1058.2.a.g	2
		1058.2.a.h	2
		1058.2.a.i	4
		1058.2.a.j	5
		1058.2.a.k	5
		1058.2.a.l	5
		1058.2.a.m	5
		1058.2.a.n	8
1058.2.c	\(\chi_{1058}(177, \cdot)\)	n/a	420	10
1058.2.e	\(\chi_{1058}(47, \cdot)\)	n/a	1012	22
1058.2.g	\(\chi_{1058}(3, \cdot)\)	n/a	10120	220

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1058))\) into lower level spaces

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