Properties

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

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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

\( 35 q + 596 q^{7} - 192 q^{8} - 1296 q^{9} + O(q^{10}) \) \( 35 q + 596 q^{7} - 192 q^{8} - 1296 q^{9} - 60 q^{10} + 1068 q^{11} + 576 q^{12} + 3144 q^{13} + 528 q^{14} - 2376 q^{15} - 1024 q^{16} - 969 q^{17} - 4860 q^{18} - 5236 q^{19} + 1968 q^{20} + 132 q^{21} + 3228 q^{23} + 9375 q^{25} + 15156 q^{27} + 9536 q^{28} + 4095 q^{29} - 18336 q^{30} - 46552 q^{31} - 55020 q^{33} - 5280 q^{34} + 30360 q^{35} + 21120 q^{36} + 53615 q^{37} + 51984 q^{38} + 89076 q^{39} + 29583 q^{41} + 144 q^{42} - 58004 q^{43} - 36480 q^{44} - 154425 q^{45} - 62880 q^{46} - 92928 q^{47} - 13544 q^{49} + 73812 q^{50} + 317064 q^{51} + 45104 q^{52} - 16668 q^{53} - 118224 q^{54} - 120660 q^{55} - 42240 q^{56} - 170184 q^{57} - 43308 q^{58} - 56496 q^{59} + 23424 q^{60} - 16965 q^{61} + 112176 q^{62} + 405612 q^{63} + 12288 q^{64} + 94467 q^{65} + 171840 q^{66} + 72140 q^{67} + 4848 q^{68} - 140352 q^{69} - 49104 q^{70} - 135768 q^{71} - 109056 q^{72} - 8440 q^{73} - 11388 q^{74} + 24420 q^{75} - 83776 q^{76} - 42936 q^{77} - 214128 q^{78} - 161760 q^{79} + 31488 q^{80} + 275940 q^{81} - 140364 q^{82} - 151536 q^{83} - 20160 q^{84} - 45009 q^{85} + 84576 q^{86} - 27816 q^{87} - 56976 q^{89} + 486000 q^{90} + 253004 q^{91} + 177024 q^{92} + 200760 q^{93} + 274800 q^{94} + 641064 q^{95} + 381284 q^{97} + 340992 q^{98} - 284436 q^{99} + O(q^{100}) \)

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

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