Space of modular forms of level 152 and weight 4

• Label: 152.4
• Level: 152
• Weight: 4
• Dimension: 1173
• Nonzero newspaces: 9
• Newform subspaces: 17
• Sturm bound: 5760
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(5760\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(152))\).

	Total	New	Old
Modular forms	2268	1241	1027
Cusp forms	2052	1173	879
Eisenstein series	216	68	148

Trace form

1173 * q - 14 * q^2 - 10 * q^3 + 6 * q^4 + 4 * q^5 - 74 * q^6 - 34 * q^7 - 98 * q^8 - 10 * q^9 + 94 * q^10 + 70 * q^11 + 94 * q^12 - 44 * q^13 - 50 * q^14 - 258 * q^15 - 50 * q^16 - 80 * q^17 - 22 * q^18 - 62 * q^19 - 260 * q^20 + 192 * q^21 + 150 * q^22 + 702 * q^23 + 206 * q^24 + 154 * q^25 - 578 * q^26 - 979 * q^27 - 210 * q^28 - 1026 * q^29 + 206 * q^30 - 684 * q^31 + 686 * q^32 + 194 * q^33 - 74 * q^34 + 1194 * q^35 - 42 * q^36 + 990 * q^37 + 178 * q^38 + 3150 * q^39 - 466 * q^40 + 1090 * q^41 + 430 * q^42 + 130 * q^43 - 354 * q^44 - 1070 * q^45 - 626 * q^46 - 3372 * q^47 - 1362 * q^48 - 1096 * q^49 + 34 * q^50 - 923 * q^51 + 1102 * q^52 + 484 * q^53 - 988 * q^54 + 478 * q^55 + 622 * q^56 - 252 * q^57 + 1644 * q^58 + 1318 * q^59 + 7266 * q^60 + 1330 * q^61 + 10508 * q^62 + 6310 * q^63 + 7038 * q^64 - 298 * q^65 + 2478 * q^66 - 718 * q^67 - 2748 * q^68 - 448 * q^69 - 10634 * q^70 - 4156 * q^71 - 16948 * q^72 - 4757 * q^73 - 13106 * q^74 - 10418 * q^75 - 13910 * q^76 - 1830 * q^77 - 13558 * q^78 - 4788 * q^79 - 5250 * q^80 - 39 * q^81 - 9208 * q^82 - 1516 * q^83 - 1562 * q^84 + 200 * q^85 + 9040 * q^86 + 4362 * q^87 + 10974 * q^88 + 3250 * q^89 + 19310 * q^90 + 10806 * q^91 + 14064 * q^92 + 2878 * q^93 + 10938 * q^94 - 7390 * q^95 + 860 * q^96 - 8780 * q^97 - 1134 * q^98 - 7097 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)

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
152.4.a	\(\chi_{152}(1, \cdot)\)	152.4.a.a	2	1
		152.4.a.b	3
		152.4.a.c	3
		152.4.a.d	5
152.4.b	\(\chi_{152}(75, \cdot)\)	152.4.b.a	2	1
		152.4.b.b	56
152.4.c	\(\chi_{152}(77, \cdot)\)	152.4.c.a	54	1
152.4.h	\(\chi_{152}(151, \cdot)\)	None	0	1
152.4.i	\(\chi_{152}(49, \cdot)\)	152.4.i.a	14	2
		152.4.i.b	16
152.4.j	\(\chi_{152}(31, \cdot)\)	None	0	2
152.4.o	\(\chi_{152}(27, \cdot)\)	152.4.o.a	4	2
		152.4.o.b	112
152.4.p	\(\chi_{152}(45, \cdot)\)	152.4.p.a	116	2
152.4.q	\(\chi_{152}(9, \cdot)\)	152.4.q.a	42	6
		152.4.q.b	48
152.4.t	\(\chi_{152}(5, \cdot)\)	152.4.t.a	348	6
152.4.v	\(\chi_{152}(3, \cdot)\)	152.4.v.a	12	6
		152.4.v.b	336
152.4.w	\(\chi_{152}(15, \cdot)\)	None	0	6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(152))\) into lower level spaces

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