Properties

Label 34.2
Level 34
Weight 2
Dimension 11
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 144
Trace bound 3

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Defining parameters

Level: \( N \) = \( 34 = 2 \cdot 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(144\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(34))\).

Total New Old
Modular forms 52 11 41
Cusp forms 21 11 10
Eisenstein series 31 0 31

Trace form

\( 11 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} + O(q^{10}) \) \( 11 q - q^{2} - 4 q^{3} - q^{4} - 6 q^{5} - 4 q^{6} - 8 q^{7} - q^{8} - 13 q^{9} - 2 q^{10} + 4 q^{11} + 4 q^{12} + 2 q^{13} + 8 q^{14} + 24 q^{15} + 3 q^{16} - q^{17} + 19 q^{18} - 4 q^{19} - 2 q^{20} + 16 q^{21} + 4 q^{22} - 8 q^{23} + 4 q^{24} + 5 q^{25} - 10 q^{26} - 16 q^{27} - 8 q^{28} - 10 q^{29} - 24 q^{30} - q^{32} - 16 q^{33} - 17 q^{34} - 16 q^{35} - 13 q^{36} - 6 q^{37} - 12 q^{38} + 8 q^{39} - 6 q^{40} + 26 q^{41} + 16 q^{42} + 12 q^{43} + 20 q^{44} + 6 q^{45} + 8 q^{46} + 32 q^{47} - 4 q^{48} + 7 q^{49} + 25 q^{50} - 4 q^{51} + 18 q^{52} + 14 q^{53} + 16 q^{54} + 8 q^{55} - 8 q^{56} + 8 q^{57} + 2 q^{58} + 20 q^{59} + 8 q^{60} - 14 q^{61} + 16 q^{62} - 8 q^{63} - q^{64} - 48 q^{65} - 40 q^{66} - 52 q^{67} - 13 q^{68} - 32 q^{69} - 16 q^{70} - 24 q^{71} + 7 q^{72} + 10 q^{73} - 2 q^{74} - 12 q^{75} - 20 q^{76} - 16 q^{77} + 8 q^{78} + 10 q^{80} - 17 q^{81} + 26 q^{82} - 12 q^{83} + 30 q^{85} - 12 q^{86} + 24 q^{87} + 20 q^{88} + 6 q^{89} - 10 q^{90} + 48 q^{91} - 8 q^{92} + 16 q^{94} + 24 q^{95} - 4 q^{96} - 2 q^{97} - 21 q^{98} + 28 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)

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
34.2.a \(\chi_{34}(1, \cdot)\) 34.2.a.a 1 1
34.2.b \(\chi_{34}(33, \cdot)\) 34.2.b.a 2 1
34.2.c \(\chi_{34}(13, \cdot)\) 34.2.c.a 2 2
34.2.c.b 2
34.2.d \(\chi_{34}(9, \cdot)\) 34.2.d.a 4 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(34))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(34)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 2}\)