Space of modular forms of level 92 and weight 2

• Label: 92.2
• Level: 92
• Weight: 2
• Dimension: 132
• Nonzero newspaces: 4
• Newform subspaces: 6
• Sturm bound: 1056
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 92 = 2^{2} \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 6 \)
Sturm bound:			\(1056\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(92))\).

	Total	New	Old
Modular forms	319	176	143
Cusp forms	210	132	78
Eisenstein series	109	44	65

Trace form

132 * q - 11 * q^2 - 11 * q^4 - 22 * q^5 - 11 * q^6 - 11 * q^8 - 22 * q^9 - 11 * q^10 - 11 * q^12 - 22 * q^13 - 11 * q^14 - 11 * q^15 - 11 * q^16 - 33 * q^17 - 11 * q^18 - 11 * q^19 - 11 * q^20 - 55 * q^21 - 22 * q^23 - 22 * q^24 - 44 * q^25 - 11 * q^26 - 33 * q^27 - 11 * q^28 - 33 * q^29 - 11 * q^30 - 11 * q^31 - 11 * q^32 - 33 * q^33 + 11 * q^34 + 22 * q^35 + 44 * q^36 + 22 * q^37 + 44 * q^38 + 44 * q^39 + 77 * q^40 + 99 * q^42 + 44 * q^43 + 66 * q^44 + 66 * q^45 + 77 * q^46 + 44 * q^47 + 77 * q^48 + 44 * q^49 + 66 * q^50 + 44 * q^51 + 99 * q^52 + 77 * q^54 + 22 * q^55 + 44 * q^56 - 11 * q^57 + 44 * q^58 - 22 * q^59 + 11 * q^60 - 66 * q^61 - 11 * q^62 - 55 * q^63 - 11 * q^64 - 99 * q^65 - 44 * q^66 - 22 * q^67 - 77 * q^69 - 22 * q^70 - 55 * q^71 + 22 * q^72 - 44 * q^73 - 22 * q^74 - 55 * q^75 - 66 * q^76 + 11 * q^77 - 121 * q^78 - 22 * q^79 - 110 * q^80 + 66 * q^81 - 77 * q^82 - 11 * q^83 - 165 * q^84 + 110 * q^85 - 121 * q^86 + 66 * q^87 - 99 * q^88 + 44 * q^89 - 198 * q^90 + 44 * q^91 - 110 * q^92 + 220 * q^93 - 88 * q^94 + 33 * q^95 - 220 * q^96 + 11 * q^97 - 99 * q^98 + 11 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)

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
92.2.a	\(\chi_{92}(1, \cdot)\)	92.2.a.a	1	1
		92.2.a.b	1
92.2.b	\(\chi_{92}(91, \cdot)\)	92.2.b.a	4	1
		92.2.b.b	6
92.2.e	\(\chi_{92}(9, \cdot)\)	92.2.e.a	20	10
92.2.h	\(\chi_{92}(7, \cdot)\)	92.2.h.a	100	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(92))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(92)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)