Space of modular forms of level 46 and weight 4

• Label: 46.4
• Level: 46
• Weight: 4
• Dimension: 66
• Nonzero newspaces: 2
• Newform subspaces: 6
• Sturm bound: 528
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(528\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(46))\).

	Total	New	Old
Modular forms	220	66	154
Cusp forms	176	66	110
Eisenstein series	44	0	44

Trace form

66 * q + 748 * q^15 + 176 * q^17 - 88 * q^18 - 220 * q^19 - 352 * q^20 - 1320 * q^21 - 484 * q^22 - 968 * q^23 - 704 * q^25 - 220 * q^26 - 132 * q^27 + 176 * q^28 + 440 * q^29 + 1496 * q^30 + 1100 * q^31 + 1936 * q^33 + 1430 * q^35 + 1188 * q^37 - 132 * q^39 - 550 * q^41 - 1716 * q^43 - 2970 * q^45 - 1892 * q^47 - 2178 * q^49 - 660 * q^51 + 242 * q^53 + 3124 * q^54 + 6996 * q^55 + 1936 * q^56 + 8052 * q^57 + 1848 * q^58 + 4950 * q^59 + 88 * q^60 - 1056 * q^61 - 1716 * q^62 - 4180 * q^63 - 8624 * q^65 - 5456 * q^66 - 2904 * q^67 - 2992 * q^68 - 7480 * q^69 - 5808 * q^70 - 6820 * q^71 - 2464 * q^72 - 2112 * q^73 - 3344 * q^74 - 22 * q^75 + 440 * q^77 + 1452 * q^78 + 5126 * q^79 + 1408 * q^80 + 8580 * q^81 + 5016 * q^82 + 8954 * q^83 + 3784 * q^84 + 7898 * q^85 + 5236 * q^86 - 4686 * q^87 - 1870 * q^89 - 4004 * q^91 + 2376 * q^95 + 11330 * q^97 + 6952 * q^98 + 11550 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)

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
46.4.a	\(\chi_{46}(1, \cdot)\)	46.4.a.a	1	1
		46.4.a.b	1
		46.4.a.c	2
		46.4.a.d	2
46.4.c	\(\chi_{46}(3, \cdot)\)	46.4.c.a	30	10
		46.4.c.b	30

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(46))\) into lower level spaces

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