Space of modular forms of level 490 and weight 6

• Label: 490.6
• Level: 490
• Weight: 6
• Dimension: 10345
• Nonzero newspaces: 12
• Sturm bound: 84672
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(84672\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(490))\).

	Total	New	Old
Modular forms	35760	10345	25415
Cusp forms	34800	10345	24455
Eisenstein series	960	0	960

Trace form

10345 * q - 4 * q^2 + 76 * q^3 - 112 * q^4 + 217 * q^5 + 784 * q^6 + 464 * q^7 - 64 * q^8 - 4219 * q^9 - 1668 * q^10 - 2516 * q^11 + 1216 * q^12 + 14714 * q^13 - 240 * q^14 - 4316 * q^15 - 768 * q^16 - 11994 * q^17 + 2060 * q^18 + 8492 * q^19 + 2640 * q^20 + 17580 * q^21 + 14640 * q^22 - 5304 * q^23 - 5376 * q^24 - 33179 * q^25 - 31928 * q^26 + 17848 * q^27 + 9344 * q^28 + 54102 * q^29 + 41712 * q^30 + 43504 * q^31 - 1024 * q^32 - 178176 * q^33 - 36680 * q^34 - 91590 * q^35 + 17040 * q^36 - 260790 * q^37 - 14048 * q^38 + 374996 * q^39 + 59200 * q^40 + 485746 * q^41 + 291888 * q^42 + 217844 * q^43 + 23168 * q^44 - 173445 * q^45 - 346000 * q^46 - 483528 * q^47 - 45056 * q^48 - 640540 * q^49 - 41012 * q^50 - 552280 * q^51 - 100128 * q^52 - 316878 * q^53 + 17808 * q^54 + 22306 * q^55 + 253440 * q^56 + 309320 * q^57 + 601896 * q^58 + 915052 * q^59 + 173856 * q^60 + 664906 * q^61 + 139312 * q^62 - 745944 * q^63 + 167936 * q^64 - 230078 * q^65 - 455360 * q^66 - 437788 * q^67 - 191904 * q^68 - 866000 * q^69 - 131208 * q^70 - 867000 * q^71 + 32960 * q^72 - 593410 * q^73 + 135368 * q^74 + 306188 * q^75 + 159680 * q^76 + 351384 * q^77 + 840640 * q^78 + 949520 * q^79 + 55552 * q^80 - 1029747 * q^81 - 525480 * q^82 + 444180 * q^83 - 139584 * q^84 - 290606 * q^85 - 1217136 * q^86 + 383736 * q^87 - 312576 * q^88 + 1258922 * q^89 + 1127724 * q^90 + 665428 * q^91 + 910464 * q^92 + 1497368 * q^93 + 1828928 * q^94 + 1173580 * q^95 + 102400 * q^96 - 1501138 * q^97 - 145536 * q^98 - 1723012 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(490))\)

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
490.6.a	\(\chi_{490}(1, \cdot)\)	490.6.a.a	1	1
		490.6.a.b	1
		490.6.a.c	1
		490.6.a.d	1
		490.6.a.e	1
		490.6.a.f	1
		490.6.a.g	1
		490.6.a.h	1
		490.6.a.i	1
		490.6.a.j	1
		490.6.a.k	1
		490.6.a.l	1
		490.6.a.m	1
		490.6.a.n	2
		490.6.a.o	2
		490.6.a.p	2
		490.6.a.q	2
		490.6.a.r	2
		490.6.a.s	2
		490.6.a.t	2
		490.6.a.u	2
		490.6.a.v	2
		490.6.a.w	2
		490.6.a.x	3
		490.6.a.y	3
		490.6.a.z	4
		490.6.a.ba	4
		490.6.a.bb	4
		490.6.a.bc	4
		490.6.a.bd	6
		490.6.a.be	6
490.6.c	\(\chi_{490}(99, \cdot)\)	n/a	102	1
490.6.e	\(\chi_{490}(361, \cdot)\)	n/a	136	2
490.6.g	\(\chi_{490}(97, \cdot)\)	n/a	200	2
490.6.i	\(\chi_{490}(79, \cdot)\)	n/a	200	2
490.6.k	\(\chi_{490}(71, \cdot)\)	n/a	576	6
490.6.l	\(\chi_{490}(117, \cdot)\)	n/a	400	4
490.6.p	\(\chi_{490}(29, \cdot)\)	n/a	840	6
490.6.q	\(\chi_{490}(11, \cdot)\)	n/a	1104	12
490.6.s	\(\chi_{490}(13, \cdot)\)	n/a	1680	12
490.6.t	\(\chi_{490}(9, \cdot)\)	n/a	1680	12
490.6.w	\(\chi_{490}(3, \cdot)\)	n/a	3360	24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(490))\) into lower level spaces

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