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Properties

Label 14.5
Level 14
Weight 5
Dimension 8
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 60
Trace bound 3

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(14))\).

Total New Old
Modular forms 30 8 22
Cusp forms 18 8 10
Eisenstein series 12 0 12

Trace form

\( 8 q - 18 q^{3} + 16 q^{4} + 54 q^{5} - 104 q^{7} - 168 q^{9} + O(q^{10}) \) \( 8 q - 18 q^{3} + 16 q^{4} + 54 q^{5} - 104 q^{7} - 168 q^{9} - 96 q^{10} + 306 q^{11} + 144 q^{12} - 288 q^{14} - 324 q^{15} + 128 q^{16} + 918 q^{17} + 768 q^{18} + 30 q^{19} + 390 q^{21} - 960 q^{22} - 1278 q^{23} - 768 q^{24} - 2872 q^{25} - 1728 q^{26} + 848 q^{28} + 4464 q^{29} + 5568 q^{30} - 546 q^{31} + 1062 q^{33} + 2142 q^{35} - 3360 q^{36} - 4342 q^{37} - 4320 q^{38} - 4080 q^{39} + 768 q^{40} + 576 q^{42} + 6032 q^{43} + 2448 q^{44} + 5724 q^{45} + 6912 q^{46} + 702 q^{47} - 10744 q^{49} - 10944 q^{50} - 10818 q^{51} - 384 q^{52} + 8586 q^{53} - 1440 q^{54} - 2304 q^{56} - 4596 q^{57} + 7680 q^{58} + 12366 q^{59} + 5904 q^{60} + 7686 q^{61} + 9528 q^{63} + 4096 q^{64} - 7056 q^{65} - 3456 q^{66} - 6110 q^{67} - 7344 q^{68} - 3360 q^{70} - 2736 q^{71} + 6144 q^{72} - 17274 q^{73} - 7776 q^{74} - 5220 q^{75} + 8442 q^{77} + 13632 q^{78} + 13570 q^{79} - 3456 q^{80} - 33966 q^{81} + 9984 q^{82} + 1104 q^{84} + 26892 q^{85} - 21888 q^{86} - 12276 q^{87} - 9984 q^{88} - 12474 q^{89} + 8256 q^{91} + 1440 q^{92} + 56934 q^{93} + 15168 q^{94} + 45774 q^{95} + 6144 q^{96} + 21888 q^{98} - 41040 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)

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
14.5.b \(\chi_{14}(13, \cdot)\) 14.5.b.a 4 1
14.5.d \(\chi_{14}(3, \cdot)\) 14.5.d.a 4 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(14))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(14)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)