Properties

Label 26.2
Level 26
Weight 2
Dimension 6
Nonzero newspaces 3
Newforms 4
Sturm bound 84
Trace bound 4

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Defining parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 4 \)
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

\(6q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{2} \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 2q^{8} \) \(\mathstrut +\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 9q^{10} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 3q^{20} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 12q^{23} \) \(\mathstrut -\mathstrut 4q^{24} \) \(\mathstrut -\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut -\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 9q^{29} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut -\mathstrut q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 11q^{36} \) \(\mathstrut -\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 16q^{38} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 9q^{41} \) \(\mathstrut +\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 12q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut -\mathstrut 4q^{48} \) \(\mathstrut -\mathstrut 25q^{49} \) \(\mathstrut -\mathstrut 4q^{50} \) \(\mathstrut -\mathstrut 6q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut -\mathstrut 4q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut -\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 23q^{61} \) \(\mathstrut +\mathstrut 4q^{62} \) \(\mathstrut +\mathstrut 20q^{63} \) \(\mathstrut +\mathstrut 2q^{64} \) \(\mathstrut +\mathstrut 9q^{65} \) \(\mathstrut +\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 15q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut -\mathstrut 12q^{70} \) \(\mathstrut +\mathstrut 11q^{72} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut +\mathstrut q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 3q^{80} \) \(\mathstrut +\mathstrut 3q^{81} \) \(\mathstrut +\mathstrut 9q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut -\mathstrut 4q^{84} \) \(\mathstrut +\mathstrut 15q^{85} \) \(\mathstrut -\mathstrut 20q^{86} \) \(\mathstrut -\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 16q^{93} \) \(\mathstrut +\mathstrut 12q^{94} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 4q^{96} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut -\mathstrut 48q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 the 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

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