Space of modular forms of level 26 and weight 2

• Label: 26.2
• Level: 26
• Weight: 2
• Dimension: 6
• Nonzero newspaces: 3
• Newform subspaces: 4
• Sturm bound: 84
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 3 \)
Newform subspaces:			\( 4 \)
Sturm bound:			\(84\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(26))\).

	Total	New	Old
Modular forms	33	6	27
Cusp forms	10	6	4
Eisenstein series	23	0	23

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)

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
26.2.a	\(\chi_{26}(1, \cdot)\)	26.2.a.a	1	1
		26.2.a.b	1
26.2.b	\(\chi_{26}(25, \cdot)\)	26.2.b.a	2	1
26.2.c	\(\chi_{26}(3, \cdot)\)	26.2.c.a	2	2
26.2.e	\(\chi_{26}(17, \cdot)\)	None	0	2

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(26))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(26)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)