Space of modular forms of level 26 and weight 6

• Label: 26.6
• Level: 26
• Weight: 6
• Dimension: 35
• Nonzero newspaces: 4
• Newform subspaces: 8
• Sturm bound: 252
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(252\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(26))\).

	Total	New	Old
Modular forms	117	35	82
Cusp forms	93	35	58
Eisenstein series	24	0	24

Trace form

35 * q + 596 * q^7 - 192 * q^8 - 1296 * q^9 - 60 * q^10 + 1068 * q^11 + 576 * q^12 + 3144 * q^13 + 528 * q^14 - 2376 * q^15 - 1024 * q^16 - 969 * q^17 - 4860 * q^18 - 5236 * q^19 + 1968 * q^20 + 132 * q^21 + 3228 * q^23 + 9375 * q^25 + 15156 * q^27 + 9536 * q^28 + 4095 * q^29 - 18336 * q^30 - 46552 * q^31 - 55020 * q^33 - 5280 * q^34 + 30360 * q^35 + 21120 * q^36 + 53615 * q^37 + 51984 * q^38 + 89076 * q^39 + 29583 * q^41 + 144 * q^42 - 58004 * q^43 - 36480 * q^44 - 154425 * q^45 - 62880 * q^46 - 92928 * q^47 - 13544 * q^49 + 73812 * q^50 + 317064 * q^51 + 45104 * q^52 - 16668 * q^53 - 118224 * q^54 - 120660 * q^55 - 42240 * q^56 - 170184 * q^57 - 43308 * q^58 - 56496 * q^59 + 23424 * q^60 - 16965 * q^61 + 112176 * q^62 + 405612 * q^63 + 12288 * q^64 + 94467 * q^65 + 171840 * q^66 + 72140 * q^67 + 4848 * q^68 - 140352 * q^69 - 49104 * q^70 - 135768 * q^71 - 109056 * q^72 - 8440 * q^73 - 11388 * q^74 + 24420 * q^75 - 83776 * q^76 - 42936 * q^77 - 214128 * q^78 - 161760 * q^79 + 31488 * q^80 + 275940 * q^81 - 140364 * q^82 - 151536 * q^83 - 20160 * q^84 - 45009 * q^85 + 84576 * q^86 - 27816 * q^87 - 56976 * q^89 + 486000 * q^90 + 253004 * q^91 + 177024 * q^92 + 200760 * q^93 + 274800 * q^94 + 641064 * q^95 + 381284 * q^97 + 340992 * q^98 - 284436 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(26))\)

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
26.6.a	\(\chi_{26}(1, \cdot)\)	26.6.a.a	1	1
		26.6.a.b	2
		26.6.a.c	2
26.6.b	\(\chi_{26}(25, \cdot)\)	26.6.b.a	2	1
		26.6.b.b	2
26.6.c	\(\chi_{26}(3, \cdot)\)	26.6.c.a	6	2
		26.6.c.b	8
26.6.e	\(\chi_{26}(17, \cdot)\)	26.6.e.a	12	2

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(26))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(26)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)