Space of modular forms of level 93 and weight 2

• Label: 93.2
• Level: 93
• Weight: 2
• Dimension: 209
• Nonzero newspaces: 8
• Newform subspaces: 18
• Sturm bound: 1280
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1280\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(93))\).

	Total	New	Old
Modular forms	380	269	111
Cusp forms	261	209	52
Eisenstein series	119	60	59

Trace form

209 * q - 3 * q^2 - 16 * q^3 - 37 * q^4 - 6 * q^5 - 18 * q^6 - 38 * q^7 - 15 * q^8 - 16 * q^9 - 48 * q^10 - 12 * q^11 - 22 * q^12 - 44 * q^13 - 24 * q^14 - 21 * q^15 - 61 * q^16 - 18 * q^17 - 18 * q^18 - 50 * q^19 - 42 * q^20 - 18 * q^21 - 6 * q^22 + 6 * q^23 + 30 * q^24 + 9 * q^25 + 18 * q^26 - 16 * q^27 + 74 * q^28 + 30 * q^29 + 42 * q^30 - q^31 + 117 * q^32 + 3 * q^33 + 36 * q^34 + 12 * q^35 - 2 * q^36 + 22 * q^37 + 6 * q^39 - 12 * q^41 - 9 * q^42 - 64 * q^43 - 84 * q^44 - 21 * q^45 - 102 * q^46 - 48 * q^47 - q^48 - 27 * q^49 + 57 * q^50 + 57 * q^51 + 22 * q^52 + 6 * q^53 + 147 * q^54 + 18 * q^55 + 150 * q^56 + 55 * q^57 + 90 * q^58 + 138 * q^60 + 118 * q^61 + 87 * q^62 + 82 * q^63 + 83 * q^64 + 96 * q^65 + 174 * q^66 - 38 * q^67 + 84 * q^68 + 51 * q^69 + 96 * q^70 + 48 * q^71 + 135 * q^72 - 44 * q^73 + 36 * q^74 + 29 * q^75 - 20 * q^76 - 36 * q^77 - 102 * q^78 - 110 * q^79 - 186 * q^80 - 76 * q^81 - 156 * q^82 - 84 * q^83 - 251 * q^84 - 138 * q^85 - 132 * q^86 - 105 * q^87 - 210 * q^88 - 90 * q^89 - 213 * q^90 - 142 * q^91 - 168 * q^92 - 166 * q^93 - 204 * q^94 - 120 * q^95 - 213 * q^96 - 128 * q^97 - 171 * q^98 - 102 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)

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
93.2.a	\(\chi_{93}(1, \cdot)\)	93.2.a.a	2	1
		93.2.a.b	3
93.2.c	\(\chi_{93}(92, \cdot)\)	93.2.c.a	8	1
93.2.e	\(\chi_{93}(25, \cdot)\)	93.2.e.a	4	2
		93.2.e.b	6
93.2.f	\(\chi_{93}(4, \cdot)\)	93.2.f.a	8	4
		93.2.f.b	16
93.2.g	\(\chi_{93}(26, \cdot)\)	93.2.g.a	2	2
		93.2.g.b	2
		93.2.g.c	2
		93.2.g.d	4
		93.2.g.e	4
		93.2.g.f	4
93.2.k	\(\chi_{93}(23, \cdot)\)	93.2.k.a	32	4
93.2.m	\(\chi_{93}(7, \cdot)\)	93.2.m.a	16	8
		93.2.m.b	24
93.2.p	\(\chi_{93}(11, \cdot)\)	93.2.p.a	8	8
		93.2.p.b	64

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(93))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(93)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 2}\)