Space of modular forms of level 46 and weight 2

• Label: 46.2
• Level: 46
• Weight: 2
• Dimension: 21
• Nonzero newspaces: 2
• Newform subspaces: 3
• Sturm bound: 264
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 3 \)
Sturm bound:			\(264\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(46))\).

	Total	New	Old
Modular forms	88	21	67
Cusp forms	45	21	24
Eisenstein series	43	0	43

Trace form

21 * q - q^2 - 4 * q^3 - q^4 - 6 * q^5 - 4 * q^6 - 8 * q^7 - q^8 - 13 * q^9 - 6 * q^10 - 12 * q^11 - 4 * q^12 - 14 * q^13 - 8 * q^14 - 2 * q^15 - q^16 + 4 * q^17 + 31 * q^18 + 2 * q^19 + 16 * q^20 + 34 * q^21 + 10 * q^22 + 21 * q^23 - 4 * q^24 + 13 * q^25 + 8 * q^26 + 26 * q^27 + 14 * q^28 - 8 * q^29 + 20 * q^30 - 10 * q^31 - q^32 - 26 * q^33 - 18 * q^34 - 26 * q^35 - 13 * q^36 + 6 * q^37 - 20 * q^38 - 12 * q^39 - 6 * q^40 - 20 * q^41 - 32 * q^42 - 12 * q^44 - 12 * q^45 - 23 * q^46 - 4 * q^47 - 4 * q^48 + 9 * q^49 - 31 * q^50 - 28 * q^51 - 14 * q^52 - 32 * q^53 - 18 * q^54 + 16 * q^55 + 14 * q^56 + 30 * q^57 + 14 * q^58 + 50 * q^59 - 2 * q^60 + 26 * q^61 + 34 * q^62 + 6 * q^63 - q^64 + 70 * q^65 + 40 * q^66 - 24 * q^67 + 26 * q^68 + 18 * q^69 + 40 * q^70 + 38 * q^71 + 31 * q^72 - 30 * q^73 + 50 * q^74 + 52 * q^75 - 20 * q^76 + 14 * q^77 + 10 * q^78 + 30 * q^79 + 16 * q^80 + 11 * q^81 + 2 * q^82 + 4 * q^83 - 10 * q^84 - 42 * q^85 - 22 * q^86 - 54 * q^87 - 12 * q^88 - 68 * q^89 - 78 * q^90 - 68 * q^91 - 23 * q^92 - 128 * q^93 - 48 * q^94 - 54 * q^95 - 4 * q^96 - 10 * q^97 - 13 * q^98 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)

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
46.2.a	\(\chi_{46}(1, \cdot)\)	46.2.a.a	1	1
46.2.c	\(\chi_{46}(3, \cdot)\)	46.2.c.a	10	10
		46.2.c.b	10

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(46))\) into lower level spaces

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