Space of modular forms of level 304 and weight 8

• Label: 304.8
• Level: 304
• Weight: 8
• Dimension: 11201
• Nonzero newspaces: 12
• Sturm bound: 46080
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(46080\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(304))\).

	Total	New	Old
Modular forms	20412	11353	9059
Cusp forms	19908	11201	8707
Eisenstein series	504	152	352

Trace form

11201 * q - 32 * q^2 - 79 * q^3 + 332 * q^4 - 317 * q^5 + 316 * q^6 - 1355 * q^7 + 1972 * q^8 - 5159 * q^9 - 25980 * q^10 - 11623 * q^11 + 54676 * q^12 + 6515 * q^13 - 44572 * q^14 + 100557 * q^15 - 26708 * q^16 + 25355 * q^17 + 58656 * q^18 - 101901 * q^19 - 92480 * q^20 - 2069 * q^21 + 88660 * q^22 + 303957 * q^23 + 118396 * q^24 - 2707 * q^25 + 71884 * q^26 - 299323 * q^27 - 440660 * q^28 - 136797 * q^29 - 55308 * q^30 + 161861 * q^31 + 497228 * q^32 - 171881 * q^33 - 1849356 * q^34 - 900595 * q^35 + 2030980 * q^36 - 208694 * q^37 + 5436 * q^38 + 2382202 * q^39 + 2243916 * q^40 + 334299 * q^41 - 249236 * q^42 - 2360311 * q^43 + 1517204 * q^44 - 147477 * q^45 - 4671356 * q^46 + 4302373 * q^47 - 8282612 * q^48 + 2758621 * q^49 + 1574352 * q^50 - 4424659 * q^51 - 820684 * q^52 - 3045997 * q^53 + 14808988 * q^54 - 2765771 * q^55 + 8186284 * q^56 + 1066631 * q^57 + 3721352 * q^58 + 11284425 * q^59 - 10294692 * q^60 - 6837497 * q^61 - 12548228 * q^62 + 1833765 * q^63 - 20904484 * q^64 - 4341929 * q^65 - 21875660 * q^66 - 7675675 * q^67 + 14807484 * q^68 - 46413 * q^69 + 44281564 * q^70 - 15466545 * q^71 + 50587860 * q^72 + 41566663 * q^73 + 26354052 * q^74 + 61306068 * q^75 - 17814296 * q^76 + 7120954 * q^77 - 75987868 * q^78 + 8748775 * q^79 - 80094580 * q^80 - 49309599 * q^81 - 45716516 * q^82 - 45953501 * q^83 + 60319372 * q^84 - 30318421 * q^85 + 108258900 * q^86 + 8112777 * q^87 + 118432748 * q^88 + 82430019 * q^89 + 67030572 * q^90 + 69930133 * q^91 - 43621908 * q^92 - 48849913 * q^93 - 154392260 * q^94 + 10595145 * q^95 - 233881000 * q^96 - 27096085 * q^97 - 43647768 * q^98 - 65082335 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(304))\)

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
304.8.a	\(\chi_{304}(1, \cdot)\)	304.8.a.a	1	1
		304.8.a.b	2
		304.8.a.c	2
		304.8.a.d	2
		304.8.a.e	4
		304.8.a.f	4
		304.8.a.g	5
		304.8.a.h	6
		304.8.a.i	6
		304.8.a.j	6
		304.8.a.k	8
		304.8.a.l	8
		304.8.a.m	9
304.8.b	\(\chi_{304}(151, \cdot)\)	None	0	1
304.8.c	\(\chi_{304}(153, \cdot)\)	None	0	1
304.8.h	\(\chi_{304}(303, \cdot)\)	304.8.h.a	2	1
		304.8.h.b	4
		304.8.h.c	20
		304.8.h.d	44
304.8.i	\(\chi_{304}(49, \cdot)\)	n/a	138	2
304.8.k	\(\chi_{304}(77, \cdot)\)	n/a	504	2
304.8.m	\(\chi_{304}(75, \cdot)\)	n/a	556	2
304.8.n	\(\chi_{304}(31, \cdot)\)	n/a	140	2
304.8.s	\(\chi_{304}(103, \cdot)\)	None	0	2
304.8.t	\(\chi_{304}(121, \cdot)\)	None	0	2
304.8.u	\(\chi_{304}(17, \cdot)\)	n/a	414	6
304.8.v	\(\chi_{304}(45, \cdot)\)	n/a	1112	4
304.8.x	\(\chi_{304}(27, \cdot)\)	n/a	1112	4
304.8.bb	\(\chi_{304}(9, \cdot)\)	None	0	6
304.8.bd	\(\chi_{304}(71, \cdot)\)	None	0	6
304.8.be	\(\chi_{304}(15, \cdot)\)	n/a	420	6
304.8.bg	\(\chi_{304}(3, \cdot)\)	n/a	3336	12
304.8.bi	\(\chi_{304}(5, \cdot)\)	n/a	3336	12

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)