Space of modular forms of level 75 and weight 3

• Label: 75.3
• Level: 75
• Weight: 3
• Dimension: 256
• Nonzero newspaces: 6
• Newform subspaces: 15
• Sturm bound: 1200
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(1200\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(75))\).

	Total	New	Old
Modular forms	456	298	158
Cusp forms	344	256	88
Eisenstein series	112	42	70

Trace form

256 * q + 8 * q^2 - 2 * q^3 - 4 * q^4 + 4 * q^5 - 2 * q^6 - 4 * q^7 - 24 * q^8 - 42 * q^9 - 44 * q^10 - 32 * q^11 - 66 * q^12 - 20 * q^13 + 6 * q^15 - 68 * q^16 - 60 * q^17 + 34 * q^18 - 124 * q^19 - 244 * q^20 - 78 * q^21 - 260 * q^22 - 152 * q^23 - 164 * q^24 - 16 * q^25 - 96 * q^26 - 98 * q^27 + 348 * q^28 + 200 * q^29 + 274 * q^30 + 340 * q^31 + 712 * q^32 + 282 * q^33 + 496 * q^34 + 260 * q^35 - 66 * q^36 - 204 * q^37 - 468 * q^38 - 282 * q^39 - 928 * q^40 - 208 * q^41 - 614 * q^42 - 548 * q^43 - 700 * q^44 - 406 * q^45 - 380 * q^46 - 416 * q^47 - 348 * q^48 - 184 * q^49 + 16 * q^50 - 180 * q^51 + 824 * q^52 + 248 * q^53 + 608 * q^54 + 604 * q^55 + 840 * q^56 + 758 * q^57 + 1544 * q^58 + 800 * q^59 + 1634 * q^60 + 188 * q^61 + 1124 * q^62 + 1052 * q^63 + 992 * q^64 + 272 * q^65 + 782 * q^66 + 284 * q^67 + 208 * q^68 + 868 * q^69 + 100 * q^70 + 544 * q^71 + 582 * q^72 + 124 * q^73 - 134 * q^75 - 1208 * q^76 - 176 * q^77 - 880 * q^78 - 964 * q^79 - 164 * q^80 - 234 * q^81 - 2196 * q^82 - 1248 * q^83 - 2362 * q^84 - 2192 * q^85 - 1112 * q^86 - 1732 * q^87 - 2804 * q^88 - 1500 * q^89 - 1494 * q^90 - 900 * q^91 - 1608 * q^92 - 920 * q^93 - 1124 * q^94 - 784 * q^95 - 190 * q^96 + 124 * q^97 + 96 * q^98 - 180 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)

We only show spaces with odd 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
75.3.c	\(\chi_{75}(26, \cdot)\)	75.3.c.a	1	1
		75.3.c.b	1
		75.3.c.c	2
		75.3.c.d	2
		75.3.c.e	2
		75.3.c.f	2
75.3.d	\(\chi_{75}(74, \cdot)\)	75.3.d.a	2	1
		75.3.d.b	4
		75.3.d.c	4
75.3.f	\(\chi_{75}(7, \cdot)\)	75.3.f.a	4	2
		75.3.f.b	4
		75.3.f.c	4
75.3.h	\(\chi_{75}(14, \cdot)\)	75.3.h.a	72	4
75.3.j	\(\chi_{75}(11, \cdot)\)	75.3.j.a	72	4
75.3.k	\(\chi_{75}(13, \cdot)\)	75.3.k.a	80	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

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