Space of modular forms of level 97 and weight 7

• Label: 97.7
• Level: 97
• Weight: 7
• Dimension: 2304
• Nonzero newspaces: 2
• Newform subspaces: 2
• Sturm bound: 5488
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 97 \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 2 \)
Sturm bound:			\(5488\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(97))\).

	Total	New	Old
Modular forms	2400	2400	0
Cusp forms	2304	2304	0
Eisenstein series	96	96	0

Trace form

2304 * q - 48 * q^2 - 48 * q^3 - 48 * q^4 - 48 * q^5 - 48 * q^6 - 48 * q^7 - 48 * q^8 - 48 * q^9 - 48 * q^10 - 48 * q^11 - 48 * q^12 - 48 * q^13 - 48 * q^14 - 48 * q^15 - 48 * q^16 - 48 * q^17 - 48 * q^18 - 48 * q^19 - 48 * q^20 - 48 * q^21 - 48 * q^22 - 48 * q^23 - 48 * q^24 - 48 * q^25 - 48 * q^26 - 48 * q^27 - 48 * q^28 - 48 * q^29 - 48 * q^30 - 48 * q^31 - 48 * q^32 - 48 * q^33 - 48 * q^34 - 48 * q^35 - 48 * q^36 - 48 * q^37 - 48 * q^38 - 48 * q^39 - 48 * q^40 - 48 * q^41 - 48 * q^42 - 48 * q^43 - 48 * q^44 - 48 * q^45 - 48 * q^46 - 48 * q^47 - 48 * q^48 - 48 * q^49 - 48 * q^50 - 48 * q^51 - 48 * q^52 - 48 * q^53 - 48 * q^54 - 48 * q^55 - 48 * q^56 - 48 * q^57 - 48 * q^58 - 48 * q^59 - 48 * q^60 - 48 * q^61 - 48 * q^62 - 48 * q^63 - 48 * q^64 - 48 * q^65 - 48 * q^66 - 48 * q^67 - 48 * q^68 - 48 * q^69 - 48 * q^70 - 48 * q^71 - 48 * q^72 - 48 * q^73 - 48 * q^74 - 48 * q^75 - 48 * q^76 - 48 * q^77 - 48 * q^78 + 11880912 * q^79 + 7569360 * q^80 - 5598768 * q^81 - 15321648 * q^82 - 4293168 * q^83 - 27371568 * q^84 - 10188336 * q^85 - 6370608 * q^86 + 933072 * q^87 + 16588752 * q^88 + 8789712 * q^89 + 30932880 * q^90 + 23569872 * q^91 + 22763472 * q^92 + 14152272 * q^93 + 9607632 * q^94 + 3844176 * q^95 - 6681648 * q^97 - 10467936 * q^98 - 18662448 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(97))\)

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
97.7.j	\(\chi_{97}(19, \cdot)\)	97.7.j.a	768	16
97.7.l	\(\chi_{97}(5, \cdot)\)	97.7.l.a	1536	32