Space of modular forms of level 310 and weight 8

• Label: 310.8
• Level: 310
• Weight: 8
• Dimension: 6150
• Nonzero newspaces: 12
• Sturm bound: 46080
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 310 = 2 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(46080\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(310))\).

	Total	New	Old
Modular forms	20400	6150	14250
Cusp forms	19920	6150	13770
Eisenstein series	480	0	480

Trace form

6150 * q - 16 * q^2 - 56 * q^3 + 384 * q^4 - 370 * q^5 - 2240 * q^6 - 208 * q^7 - 1024 * q^8 + 16382 * q^9 - 720 * q^10 - 25320 * q^11 - 3584 * q^12 + 17204 * q^13 + 11392 * q^14 + 62920 * q^15 - 40960 * q^16 - 40548 * q^17 + 22448 * q^18 - 218200 * q^19 - 8320 * q^20 - 829940 * q^21 + 874848 * q^22 + 1050564 * q^23 + 86016 * q^24 - 515950 * q^25 - 838400 * q^26 - 1504820 * q^27 + 411648 * q^28 + 1536300 * q^29 + 743520 * q^30 + 3375720 * q^31 - 65536 * q^32 - 939672 * q^33 - 2797408 * q^34 - 2300060 * q^35 - 4421760 * q^36 - 4762768 * q^37 + 260320 * q^38 + 7684244 * q^39 - 209920 * q^40 + 3066720 * q^41 - 4932512 * q^42 - 8040396 * q^43 + 2938368 * q^44 + 6109590 * q^45 - 1139840 * q^46 - 851328 * q^47 - 229376 * q^48 + 4836498 * q^49 - 4973200 * q^50 + 20111660 * q^51 + 1101056 * q^52 - 9390576 * q^53 + 11840640 * q^54 - 8296900 * q^55 - 942080 * q^56 - 12960460 * q^57 - 3704160 * q^58 + 2909580 * q^59 - 4922880 * q^60 + 49571560 * q^61 + 641024 * q^62 + 38635904 * q^63 + 1572864 * q^64 - 8040770 * q^65 - 2497280 * q^66 - 12207748 * q^67 - 2595072 * q^68 - 71766716 * q^69 - 5567360 * q^70 + 2069400 * q^71 + 1436672 * q^72 + 29656424 * q^73 + 4578592 * q^74 + 10948640 * q^75 - 3813120 * q^76 + 88723704 * q^77 + 142898656 * q^78 + 61162980 * q^79 + 7208960 * q^80 - 51076650 * q^81 - 55322592 * q^82 - 245564076 * q^83 - 87593472 * q^84 - 61947340 * q^85 - 104300480 * q^86 - 65907840 * q^87 + 10862592 * q^88 + 158745360 * q^89 + 131477520 * q^90 + 174235820 * q^91 + 9225216 * q^92 + 363648544 * q^93 + 37225792 * q^94 + 22681240 * q^95 - 9175040 * q^96 - 44410728 * q^97 - 183156048 * q^98 - 228330436 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(310))\)

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
310.8.a	\(\chi_{310}(1, \cdot)\)	310.8.a.a	6	1
		310.8.a.b	8
		310.8.a.c	8
		310.8.a.d	9
		310.8.a.e	9
		310.8.a.f	10
		310.8.a.g	10
		310.8.a.h	10
310.8.b	\(\chi_{310}(249, \cdot)\)	n/a	104	1
310.8.e	\(\chi_{310}(191, \cdot)\)	n/a	152	2
310.8.f	\(\chi_{310}(123, \cdot)\)	n/a	224	2
310.8.h	\(\chi_{310}(101, \cdot)\)	n/a	288	4
310.8.k	\(\chi_{310}(129, \cdot)\)	n/a	224	2
310.8.n	\(\chi_{310}(39, \cdot)\)	n/a	448	4
310.8.p	\(\chi_{310}(37, \cdot)\)	n/a	448	4
310.8.q	\(\chi_{310}(41, \cdot)\)	n/a	608	8
310.8.s	\(\chi_{310}(23, \cdot)\)	n/a	896	8
310.8.t	\(\chi_{310}(9, \cdot)\)	n/a	896	8
310.8.w	\(\chi_{310}(3, \cdot)\)	n/a	1792	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(310))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(310)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)