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Properties

Label 2.14
Level 2
Weight 14
Dimension 2
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 14 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_1(2))\).

Total New Old
Modular forms 4 2 2
Cusp forms 2 2 0
Eisenstein series 2 0 2

Trace form

\( 2 q - 600 q^{3} + 8192 q^{4} - 53460 q^{5} + 196608 q^{6} - 369200 q^{7} + 1709946 q^{9} + O(q^{10}) \) \( 2 q - 600 q^{3} + 8192 q^{4} - 53460 q^{5} + 196608 q^{6} - 369200 q^{7} + 1709946 q^{9} - 3932160 q^{10} + 4084344 q^{11} - 2457600 q^{12} - 2845700 q^{13} + 31850496 q^{14} - 78333840 q^{15} + 33554432 q^{16} + 131681700 q^{17} - 117964800 q^{18} - 106794680 q^{19} - 218972160 q^{20} + 875171904 q^{21} + 54067200 q^{22} - 1792659600 q^{23} + 805306368 q^{24} + 875016350 q^{25} + 1210318848 q^{26} - 2387545200 q^{27} - 1512243200 q^{28} + 4368056220 q^{29} - 4075683840 q^{30} + 2771239744 q^{31} + 72309600 q^{33} + 674758656 q^{34} - 5419522080 q^{35} + 7003938816 q^{36} - 22590929300 q^{37} + 24286003200 q^{38} + 29901362352 q^{39} - 16106127360 q^{40} - 52429051116 q^{41} - 45848985600 q^{42} + 110529014200 q^{43} + 16729473024 q^{44} + 10916247420 q^{45} - 37149868032 q^{46} - 95668711200 q^{47} - 10066329600 q^{48} - 1788972366 q^{49} + 210213273600 q^{50} - 23310302256 q^{51} - 11655987200 q^{52} - 98507315700 q^{53} - 109972684800 q^{54} - 135126771120 q^{55} + 130459631616 q^{56} + 614902480800 q^{57} - 393550233600 q^{58} - 187535765160 q^{59} - 320855408640 q^{60} + 546582757084 q^{61} + 410871398400 q^{62} - 774303174000 q^{63} + 137438953472 q^{64} - 504887486040 q^{65} + 385287192576 q^{66} + 483821583400 q^{67} + 539368243200 q^{68} - 353798952768 q^{69} - 125487022080 q^{70} - 760208731056 q^{71} - 483183820800 q^{72} - 259603126700 q^{73} - 1061067423744 q^{74} + 4782613661400 q^{75} - 437431009280 q^{76} - 543756628800 q^{77} - 642839347200 q^{78} - 1748577467360 q^{79} - 896909967360 q^{80} - 4649287111758 q^{81} + 3006765465600 q^{82} + 7424547885000 q^{83} + 3584704118784 q^{84} - 3843735995880 q^{85} - 448279805952 q^{86} - 10755622472400 q^{87} + 221459251200 q^{88} + 6497185492980 q^{89} - 208691527680 q^{90} + 5231035901024 q^{91} - 7342733721600 q^{92} + 9029541638400 q^{93} - 734525128704 q^{94} - 8802659739600 q^{95} + 3298534883328 q^{96} + 3993560066500 q^{97} - 11759203123200 q^{98} + 2713436162712 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_1(2))\)

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
2.14.a \(\chi_{2}(1, \cdot)\) 2.14.a.a 1 1
2.14.a.b 1