Space of modular forms of level 490 and weight 4

• Label: 490.4
• Level: 490
• Weight: 4
• Dimension: 6207
• Nonzero newspaces: 12
• Sturm bound: 56448
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(56448\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(490))\).

	Total	New	Old
Modular forms	21648	6207	15441
Cusp forms	20688	6207	14481
Eisenstein series	960	0	960

Trace form

6207 * q + 2 * q^2 + 40 * q^3 - 4 * q^4 - 53 * q^5 - 152 * q^6 - 96 * q^7 + 8 * q^8 + 251 * q^9 + 122 * q^10 + 124 * q^11 + 160 * q^12 + 206 * q^13 + 264 * q^14 - 104 * q^15 + 48 * q^16 - 534 * q^17 - 598 * q^18 - 220 * q^19 - 180 * q^20 - 144 * q^21 - 840 * q^22 - 1044 * q^23 - 288 * q^24 - 2393 * q^25 - 500 * q^26 - 944 * q^27 + 48 * q^28 + 2418 * q^29 + 2232 * q^30 + 2848 * q^31 + 32 * q^32 + 5304 * q^33 + 2020 * q^34 + 2028 * q^35 + 2364 * q^36 - 5242 * q^37 - 2864 * q^38 - 5464 * q^39 - 840 * q^40 - 5234 * q^41 + 72 * q^42 - 2656 * q^43 + 608 * q^44 - 3585 * q^45 + 5240 * q^46 + 1596 * q^47 + 832 * q^48 + 15948 * q^49 + 3562 * q^50 + 17864 * q^51 + 2024 * q^52 + 10134 * q^53 + 4200 * q^54 - 2504 * q^55 - 576 * q^56 - 10336 * q^57 - 9252 * q^58 - 14948 * q^59 - 4536 * q^60 - 16254 * q^61 - 10472 * q^62 - 15648 * q^63 + 1472 * q^64 + 2494 * q^65 - 1952 * q^66 + 2840 * q^67 - 2136 * q^68 + 7096 * q^69 - 756 * q^70 + 1440 * q^71 - 2392 * q^72 + 8930 * q^73 + 5036 * q^74 + 5156 * q^75 + 4976 * q^76 + 5388 * q^77 + 5536 * q^78 + 1448 * q^79 - 848 * q^80 - 37653 * q^81 - 4812 * q^82 - 29784 * q^83 - 1824 * q^84 - 21842 * q^85 - 6552 * q^86 - 34896 * q^87 - 2592 * q^88 - 17410 * q^89 - 14286 * q^90 + 3564 * q^91 - 6192 * q^92 + 29360 * q^93 - 5728 * q^94 + 15448 * q^95 + 640 * q^96 + 14330 * q^97 + 3648 * q^98 + 44564 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(490))\)

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
490.4.a	\(\chi_{490}(1, \cdot)\)	490.4.a.a	1	1
		490.4.a.b	1
		490.4.a.c	1
		490.4.a.d	1
		490.4.a.e	1
		490.4.a.f	1
		490.4.a.g	1
		490.4.a.h	1
		490.4.a.i	1
		490.4.a.j	1
		490.4.a.k	1
		490.4.a.l	1
		490.4.a.m	1
		490.4.a.n	1
		490.4.a.o	1
		490.4.a.p	2
		490.4.a.q	2
		490.4.a.r	2
		490.4.a.s	2
		490.4.a.t	2
		490.4.a.u	2
		490.4.a.v	3
		490.4.a.w	3
		490.4.a.x	4
		490.4.a.y	4
490.4.c	\(\chi_{490}(99, \cdot)\)	490.4.c.a	2	1
		490.4.c.b	2
		490.4.c.c	6
		490.4.c.d	8
		490.4.c.e	12
		490.4.c.f	12
		490.4.c.g	20
490.4.e	\(\chi_{490}(361, \cdot)\)	490.4.e.a	2	2
		490.4.e.b	2
		490.4.e.c	2
		490.4.e.d	2
		490.4.e.e	2
		490.4.e.f	2
		490.4.e.g	2
		490.4.e.h	2
		490.4.e.i	2
		490.4.e.j	2
		490.4.e.k	2
		490.4.e.l	2
		490.4.e.m	2
		490.4.e.n	2
		490.4.e.o	2
		490.4.e.p	2
		490.4.e.q	2
		490.4.e.r	2
		490.4.e.s	2
		490.4.e.t	4
		490.4.e.u	4
		490.4.e.v	4
		490.4.e.w	4
		490.4.e.x	4
		490.4.e.y	6
		490.4.e.z	8
		490.4.e.ba	8
490.4.g	\(\chi_{490}(97, \cdot)\)	n/a	120	2
490.4.i	\(\chi_{490}(79, \cdot)\)	n/a	120	2
490.4.k	\(\chi_{490}(71, \cdot)\)	n/a	336	6
490.4.l	\(\chi_{490}(117, \cdot)\)	n/a	240	4
490.4.p	\(\chi_{490}(29, \cdot)\)	n/a	504	6
490.4.q	\(\chi_{490}(11, \cdot)\)	n/a	672	12
490.4.s	\(\chi_{490}(13, \cdot)\)	n/a	1008	12
490.4.t	\(\chi_{490}(9, \cdot)\)	n/a	1008	12
490.4.w	\(\chi_{490}(3, \cdot)\)	n/a	2016	24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(490))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(490)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)