Space of modular forms of level 75 and weight 4

• Label: 75.4
• Level: 75
• Weight: 4
• Dimension: 394
• Nonzero newspaces: 6
• Newform subspaces: 17
• Sturm bound: 1600
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1600\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(75))\).

	Total	New	Old
Modular forms	656	434	222
Cusp forms	544	394	150
Eisenstein series	112	40	72

Trace form

394 * q - 8 * q^2 + 2 * q^3 + 28 * q^4 - 6 * q^5 - 18 * q^6 + 20 * q^7 + 72 * q^8 + 26 * q^9 + 76 * q^10 + 112 * q^11 - 226 * q^12 - 348 * q^13 - 528 * q^14 - 184 * q^15 - 132 * q^16 + 560 * q^17 + 578 * q^18 + 732 * q^19 + 156 * q^20 + 918 * q^21 - 420 * q^22 - 304 * q^23 - 864 * q^24 - 1546 * q^25 - 1344 * q^26 - 1414 * q^27 - 2852 * q^28 - 1736 * q^29 - 886 * q^30 - 580 * q^31 + 2008 * q^32 + 974 * q^33 + 4416 * q^34 + 2240 * q^35 + 1886 * q^36 + 3570 * q^37 + 5764 * q^38 + 3678 * q^39 + 4232 * q^40 + 1648 * q^41 + 114 * q^42 - 1484 * q^43 - 4116 * q^44 - 2456 * q^45 - 5260 * q^46 - 3904 * q^47 - 4640 * q^48 - 4710 * q^49 - 8224 * q^50 - 1960 * q^51 - 7888 * q^52 - 3554 * q^53 - 3348 * q^54 - 1516 * q^55 - 840 * q^56 - 1442 * q^57 + 3088 * q^58 + 2288 * q^59 + 74 * q^60 + 1052 * q^61 + 10076 * q^62 - 374 * q^63 + 7192 * q^64 + 1222 * q^65 - 762 * q^66 - 268 * q^67 - 304 * q^68 + 2782 * q^69 + 1540 * q^70 + 1376 * q^71 + 13758 * q^72 + 5940 * q^73 + 6752 * q^74 + 9396 * q^75 + 8808 * q^76 + 3456 * q^77 + 8380 * q^78 + 3020 * q^79 - 1004 * q^80 - 286 * q^81 + 8716 * q^82 + 11104 * q^83 + 4358 * q^84 + 12538 * q^85 + 1192 * q^86 + 1962 * q^87 + 3532 * q^88 + 3402 * q^89 - 10894 * q^90 - 7540 * q^91 - 10712 * q^92 - 13418 * q^93 - 28932 * q^94 - 15944 * q^95 - 15150 * q^96 - 31028 * q^97 - 27968 * q^98 - 2016 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.4.a	\(\chi_{75}(1, \cdot)\)	75.4.a.a	1	1
		75.4.a.b	1
		75.4.a.c	2
		75.4.a.d	2
		75.4.a.e	2
		75.4.a.f	2
75.4.b	\(\chi_{75}(49, \cdot)\)	75.4.b.a	2	1
		75.4.b.b	2
		75.4.b.c	4
75.4.e	\(\chi_{75}(32, \cdot)\)	75.4.e.a	4	2
		75.4.e.b	4
		75.4.e.c	8
		75.4.e.d	16
75.4.g	\(\chi_{75}(16, \cdot)\)	75.4.g.a	28	4
		75.4.g.b	28
75.4.i	\(\chi_{75}(4, \cdot)\)	75.4.i.a	64	4
75.4.l	\(\chi_{75}(2, \cdot)\)	75.4.l.a	224	8

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)