Space of modular forms of level 2401 and weight 4

• Label: 2401.4
• Level: 2401
• Weight: 4
• Dimension: 675540
• Nonzero newspaces: 8
• Sturm bound: 1882384
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 2401 = 7^{4} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(1882384\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2401))\).

	Total	New	Old
Modular forms	708246	679212	29034
Cusp forms	703542	675540	28002
Eisenstein series	4704	3672	1032

Trace form

675540 * q - 756 * q^2 - 756 * q^3 - 756 * q^4 - 756 * q^5 - 756 * q^6 - 882 * q^7 - 1404 * q^8 - 756 * q^9 - 756 * q^10 - 756 * q^11 - 756 * q^12 - 756 * q^13 - 882 * q^14 - 1404 * q^15 - 756 * q^16 - 756 * q^17 - 756 * q^18 - 756 * q^19 - 756 * q^20 - 882 * q^21 - 1404 * q^22 - 756 * q^23 - 756 * q^24 - 756 * q^25 - 756 * q^26 - 756 * q^27 - 882 * q^28 - 1404 * q^29 - 756 * q^30 - 756 * q^31 - 756 * q^32 - 756 * q^33 - 756 * q^34 - 882 * q^35 - 3348 * q^36 - 3108 * q^37 - 3360 * q^38 - 2814 * q^39 - 3780 * q^40 - 1092 * q^41 - 882 * q^42 - 648 * q^43 + 2772 * q^44 + 3024 * q^45 + 4536 * q^46 + 1176 * q^47 + 6615 * q^48 - 882 * q^49 + 1809 * q^50 + 2772 * q^51 + 4788 * q^52 + 420 * q^53 + 1512 * q^54 - 126 * q^55 - 882 * q^56 - 2412 * q^57 - 4284 * q^58 - 3360 * q^59 - 11340 * q^60 - 6048 * q^61 - 6384 * q^62 - 882 * q^63 - 6012 * q^64 - 756 * q^65 - 756 * q^66 - 756 * q^67 - 756 * q^68 - 756 * q^69 - 882 * q^70 - 1404 * q^71 - 756 * q^72 - 756 * q^73 - 756 * q^74 - 756 * q^75 - 756 * q^76 - 882 * q^77 - 5292 * q^78 - 756 * q^79 - 13923 * q^80 - 15456 * q^81 - 15771 * q^82 - 10248 * q^83 - 882 * q^84 - 6360 * q^85 - 5901 * q^86 - 2940 * q^87 + 861 * q^88 + 1344 * q^89 + 15603 * q^90 - 882 * q^91 + 8445 * q^92 + 18648 * q^93 + 15309 * q^94 + 14532 * q^95 + 32991 * q^96 + 7371 * q^97 - 882 * q^98 + 13905 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2401))\)

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
2401.4.a	\(\chi_{2401}(1, \cdot)\)	2401.4.a.a	33	1
		2401.4.a.b	33
		2401.4.a.c	39
		2401.4.a.d	39
		2401.4.a.e	66
		2401.4.a.f	78
		2401.4.a.g	78
		2401.4.a.h	120
2401.4.c	\(\chi_{2401}(1047, \cdot)\)	n/a	972	2
2401.4.e	\(\chi_{2401}(344, \cdot)\)	n/a	2934	6
2401.4.g	\(\chi_{2401}(18, \cdot)\)	n/a	5868	12
2401.4.i	\(\chi_{2401}(50, \cdot)\)	n/a	20370	42
2401.4.k	\(\chi_{2401}(30, \cdot)\)	n/a	40740	84
2401.4.m	\(\chi_{2401}(8, \cdot)\)	n/a	201390	294
2401.4.o	\(\chi_{2401}(2, \cdot)\)	n/a	402780	588

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2401))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2401)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(343))\)\(^{\oplus 2}\)