Properties

Label 26.8
Level 26
Weight 8
Dimension 47
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(26))\).

Total New Old
Modular forms 159 47 112
Cusp forms 135 47 88
Eisenstein series 24 0 24

Trace form

\( 47 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} + 996 q^{7} - 512 q^{8} + 15750 q^{9} + O(q^{10}) \) \( 47 q + 16 q^{2} - 24 q^{3} - 128 q^{4} + 420 q^{5} + 192 q^{6} + 996 q^{7} - 512 q^{8} + 15750 q^{9} + 6600 q^{10} - 10092 q^{11} - 8448 q^{12} - 31310 q^{13} + 27104 q^{14} + 87336 q^{15} + 8192 q^{16} + 41973 q^{17} - 120168 q^{18} - 163020 q^{19} + 21312 q^{20} + 413004 q^{21} + 17472 q^{22} - 152388 q^{23} + 12288 q^{24} - 166325 q^{25} + 11056 q^{26} - 52668 q^{27} + 63744 q^{28} - 298623 q^{29} - 848064 q^{30} - 221736 q^{31} + 65536 q^{32} + 655692 q^{33} + 1009248 q^{34} + 321960 q^{35} - 179328 q^{36} - 668535 q^{37} - 2614432 q^{38} - 1646004 q^{39} - 215040 q^{40} - 65751 q^{41} + 1836384 q^{42} + 3668308 q^{43} + 2128896 q^{44} + 5560845 q^{45} + 1945920 q^{46} - 1782336 q^{47} - 98304 q^{48} - 5993146 q^{49} - 2235176 q^{50} - 1207752 q^{51} + 1605056 q^{52} - 3267936 q^{53} - 4695264 q^{54} + 2957820 q^{55} + 2766848 q^{56} + 13936728 q^{57} + 3821736 q^{58} + 2269224 q^{59} + 1688064 q^{60} - 3521671 q^{61} - 1794016 q^{62} - 24441732 q^{63} - 1310720 q^{64} - 26063475 q^{65} - 8822400 q^{66} + 2874660 q^{67} - 1742784 q^{68} + 26499360 q^{69} + 7690656 q^{70} + 27416952 q^{71} + 7627776 q^{72} + 21801540 q^{73} + 13856264 q^{74} - 31980900 q^{75} - 10433280 q^{76} - 68319144 q^{77} - 35333088 q^{78} - 16167136 q^{79} + 1363968 q^{80} + 47626506 q^{81} + 40094664 q^{82} + 34850664 q^{83} + 10583808 q^{84} + 63193329 q^{85} - 10860544 q^{86} + 7572360 q^{87} + 1118208 q^{88} - 22841076 q^{89} - 36875520 q^{90} - 61186356 q^{91} - 22783488 q^{92} - 51075672 q^{93} + 1649376 q^{94} + 13611576 q^{95} + 786432 q^{96} + 100092648 q^{97} + 34654992 q^{98} + 39481812 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(26))\)

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
26.8.a \(\chi_{26}(1, \cdot)\) 26.8.a.a 1 1
26.8.a.b 1
26.8.a.c 1
26.8.a.d 2
26.8.a.e 2
26.8.b \(\chi_{26}(25, \cdot)\) 26.8.b.a 10 1
26.8.c \(\chi_{26}(3, \cdot)\) 26.8.c.a 6 2
26.8.c.b 8
26.8.e \(\chi_{26}(17, \cdot)\) 26.8.e.a 16 2

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(26))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(26)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 1}\)