Space of modular forms of level 75 and weight 7

• Label: 75.7
• Level: 75
• Weight: 7
• Dimension: 809
• Nonzero newspaces: 6
• Newform subspaces: 16
• Sturm bound: 2800
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 16 \)
Sturm bound:			\(2800\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(75))\).

	Total	New	Old
Modular forms	1256	851	405
Cusp forms	1144	809	335
Eisenstein series	112	42	70

Trace form

809 * q - 32 * q^2 + 31 * q^3 + 60 * q^4 - 136 * q^5 - 1106 * q^6 + 1910 * q^7 + 6936 * q^8 + 2007 * q^9 - 6064 * q^10 - 6496 * q^11 - 11154 * q^12 + 1046 * q^13 + 7296 * q^15 + 2012 * q^16 + 20040 * q^17 + 41494 * q^18 + 12454 * q^19 - 61844 * q^20 - 72912 * q^21 - 196580 * q^22 - 83392 * q^23 + 45916 * q^24 + 133364 * q^25 + 81312 * q^26 - 83321 * q^27 + 209564 * q^28 + 49600 * q^29 - 25166 * q^30 - 165378 * q^31 - 320488 * q^32 - 10458 * q^33 + 197996 * q^34 + 362080 * q^35 - 224082 * q^36 - 370 * q^37 - 271908 * q^38 - 188304 * q^39 + 753912 * q^40 - 356384 * q^41 + 87946 * q^42 - 833362 * q^43 - 1423100 * q^44 - 817606 * q^45 - 137660 * q^46 - 449056 * q^47 + 1218300 * q^48 + 2051643 * q^49 + 1983956 * q^50 + 1134900 * q^51 + 1726168 * q^52 - 3632 * q^53 - 852472 * q^54 + 607324 * q^55 - 1224120 * q^56 - 1571248 * q^57 - 4501256 * q^58 - 2525600 * q^59 - 1787206 * q^60 - 483834 * q^61 + 554644 * q^62 + 1499168 * q^63 + 10355296 * q^64 + 2707372 * q^65 + 1366286 * q^66 - 817282 * q^67 - 1523392 * q^68 - 2093042 * q^69 - 3729740 * q^70 - 1663168 * q^71 - 1520418 * q^72 - 3017890 * q^73 + 1384336 * q^75 + 6613768 * q^76 + 6411104 * q^77 + 5393840 * q^78 + 4849294 * q^79 + 1124876 * q^80 - 3547281 * q^81 - 8945876 * q^82 - 4038528 * q^83 - 4872874 * q^84 + 5992328 * q^85 - 4823416 * q^86 + 129638 * q^87 + 1033036 * q^88 + 2755500 * q^89 + 7656006 * q^90 + 8247584 * q^91 + 518712 * q^92 - 363704 * q^93 - 7812964 * q^94 - 9134624 * q^95 - 3220030 * q^96 - 11473282 * q^97 - 20730984 * q^98 - 10850100 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(75))\)

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
75.7.c	\(\chi_{75}(26, \cdot)\)	75.7.c.a	1	1
		75.7.c.b	2
		75.7.c.c	8
		75.7.c.d	8
		75.7.c.e	8
		75.7.c.f	8
75.7.d	\(\chi_{75}(74, \cdot)\)	75.7.d.a	2	1
		75.7.d.b	16
		75.7.d.c	16
75.7.f	\(\chi_{75}(7, \cdot)\)	75.7.f.a	8	2
		75.7.f.b	8
		75.7.f.c	8
		75.7.f.d	12
75.7.h	\(\chi_{75}(14, \cdot)\)	75.7.h.a	232	4
75.7.j	\(\chi_{75}(11, \cdot)\)	75.7.j.a	232	4
75.7.k	\(\chi_{75}(13, \cdot)\)	75.7.k.a	240	8

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(75))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(75)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)