Space of modular forms of level 152 and weight 8

• Label: 152.8
• Level: 152
• Weight: 8
• Dimension: 2783
• Nonzero newspaces: 9
• Sturm bound: 11520
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 9 \)
Sturm bound:			\(11520\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(152))\).

	Total	New	Old
Modular forms	5148	2851	2297
Cusp forms	4932	2783	2149
Eisenstein series	216	68	148

Trace form

2783 * q - 30 * q^2 + 62 * q^3 - 250 * q^4 - 696 * q^5 - 554 * q^6 + 4718 * q^7 - 3042 * q^8 - 3436 * q^9 + 3294 * q^10 + 11358 * q^11 + 8158 * q^12 + 9320 * q^13 - 24114 * q^14 - 87378 * q^15 - 70706 * q^16 + 51900 * q^17 + 178106 * q^18 + 1334 * q^19 + 229500 * q^20 + 31104 * q^21 - 305738 * q^22 - 163986 * q^23 - 565042 * q^24 + 7844 * q^25 + 633918 * q^26 + 55649 * q^27 + 961582 * q^28 + 152706 * q^29 - 1643314 * q^30 - 667316 * q^31 - 1634130 * q^32 - 1898398 * q^33 + 2018198 * q^34 + 1561434 * q^35 + 2507094 * q^36 + 1855314 * q^37 - 974142 * q^38 - 295674 * q^39 - 1908946 * q^40 - 1479810 * q^41 + 2186158 * q^42 - 3204886 * q^43 + 2192670 * q^44 - 444650 * q^45 - 1859698 * q^46 - 25428 * q^47 - 1707858 * q^48 + 3379390 * q^49 + 297234 * q^50 - 6377687 * q^51 - 1647922 * q^52 - 4218360 * q^53 + 2193476 * q^54 + 8847598 * q^55 + 4937838 * q^56 + 2477220 * q^57 - 6261524 * q^58 + 3727134 * q^59 + 19066146 * q^60 - 2697442 * q^61 - 18973572 * q^62 - 34129034 * q^63 - 19503490 * q^64 - 9301818 * q^65 + 12347118 * q^66 + 18552538 * q^67 + 30421860 * q^68 + 13587584 * q^69 + 55610806 * q^70 + 27831252 * q^71 - 10142740 * q^72 - 11095461 * q^73 - 69162546 * q^74 - 74547818 * q^75 - 82087126 * q^76 - 27345342 * q^77 - 12895510 * q^78 - 28716404 * q^79 + 55962750 * q^80 + 26245155 * q^81 + 129424408 * q^82 + 48236844 * q^83 + 123822694 * q^84 + 12163600 * q^85 + 37658880 * q^86 + 64333050 * q^87 - 85030946 * q^88 - 66198138 * q^89 - 170342290 * q^90 - 72297258 * q^91 - 35917488 * q^92 - 7182026 * q^93 + 116707866 * q^94 - 75935670 * q^95 - 42804388 * q^96 + 45299808 * q^97 + 29966466 * q^98 + 81624907 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.8.a	\(\chi_{152}(1, \cdot)\)	152.8.a.a	6	1
		152.8.a.b	8
		152.8.a.c	8
		152.8.a.d	9
152.8.b	\(\chi_{152}(75, \cdot)\)	n/a	138	1
152.8.c	\(\chi_{152}(77, \cdot)\)	n/a	126	1
152.8.h	\(\chi_{152}(151, \cdot)\)	None	0	1
152.8.i	\(\chi_{152}(49, \cdot)\)	152.8.i.a	34	2
		152.8.i.b	36
152.8.j	\(\chi_{152}(31, \cdot)\)	None	0	2
152.8.o	\(\chi_{152}(27, \cdot)\)	n/a	276	2
152.8.p	\(\chi_{152}(45, \cdot)\)	n/a	276	2
152.8.q	\(\chi_{152}(9, \cdot)\)	n/a	210	6
152.8.t	\(\chi_{152}(5, \cdot)\)	n/a	828	6
152.8.v	\(\chi_{152}(3, \cdot)\)	n/a	828	6
152.8.w	\(\chi_{152}(15, \cdot)\)	None	0	6

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

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