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Properties

Label 14.9
Level 14
Weight 9
Dimension 16
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 108
Trace bound 1

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(108\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(14))\).

Total New Old
Modular forms 54 16 38
Cusp forms 42 16 26
Eisenstein series 12 0 12

Trace form

\( 16 q + 162 q^{3} - 256 q^{4} + 1674 q^{5} - 7384 q^{7} + 9912 q^{9} + O(q^{10}) \) \( 16 q + 162 q^{3} - 256 q^{4} + 1674 q^{5} - 7384 q^{7} + 9912 q^{9} + 17664 q^{10} - 3258 q^{11} - 20736 q^{12} + 94464 q^{14} - 268524 q^{15} - 32768 q^{16} + 173178 q^{17} + 288768 q^{18} + 405978 q^{19} - 1070862 q^{21} - 606720 q^{22} - 735138 q^{23} + 98304 q^{24} + 2055568 q^{25} + 1958400 q^{26} - 1033472 q^{28} - 4038192 q^{29} - 49152 q^{30} + 4520250 q^{31} + 4954482 q^{33} - 6926598 q^{35} - 7795200 q^{36} - 2360882 q^{37} + 1278720 q^{38} + 11564376 q^{39} - 2260992 q^{40} + 4778496 q^{42} - 3775328 q^{43} - 417024 q^{44} - 8415396 q^{45} + 5405184 q^{46} + 18385002 q^{47} - 2727584 q^{49} - 13824 q^{50} - 2997990 q^{51} - 3369984 q^{52} - 55267794 q^{53} - 19646208 q^{54} + 9142272 q^{56} + 69572964 q^{57} + 43837440 q^{58} + 31163922 q^{59} + 14678784 q^{60} - 85390158 q^{61} + 45142728 q^{63} + 33554432 q^{64} - 58397976 q^{65} - 111873024 q^{66} - 50070610 q^{67} - 22166784 q^{68} + 70129920 q^{70} + 107675136 q^{71} + 36962304 q^{72} + 9414786 q^{73} + 35880192 q^{74} + 9837540 q^{75} - 55405098 q^{77} - 142192128 q^{78} + 84620030 q^{79} - 27426816 q^{80} - 160465770 q^{81} - 93259776 q^{82} + 69630720 q^{84} + 25291332 q^{85} + 59535360 q^{86} + 334229724 q^{87} + 103120896 q^{88} + 323014482 q^{89} - 228702576 q^{91} - 155128320 q^{92} - 419586606 q^{93} - 443440128 q^{94} + 52049394 q^{95} - 12582912 q^{96} + 243514368 q^{98} - 122686128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(14))\)

We only show spaces with odd 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
14.9.b \(\chi_{14}(13, \cdot)\) 14.9.b.a 4 1
14.9.d \(\chi_{14}(3, \cdot)\) 14.9.d.a 12 2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{9}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{9}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)