Properties

Label 2.10
Level 2
Weight 10
Dimension 1
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(2))\).

Total New Old
Modular forms 3 1 2
Cusp forms 1 1 0
Eisenstein series 2 0 2

Trace form

\( q + 16 q^{2} - 156 q^{3} + 256 q^{4} + 870 q^{5} - 2496 q^{6} - 952 q^{7} + 4096 q^{8} + 4653 q^{9} + O(q^{10}) \) \( q + 16 q^{2} - 156 q^{3} + 256 q^{4} + 870 q^{5} - 2496 q^{6} - 952 q^{7} + 4096 q^{8} + 4653 q^{9} + 13920 q^{10} - 56148 q^{11} - 39936 q^{12} + 178094 q^{13} - 15232 q^{14} - 135720 q^{15} + 65536 q^{16} - 247662 q^{17} + 74448 q^{18} + 315380 q^{19} + 222720 q^{20} + 148512 q^{21} - 898368 q^{22} + 204504 q^{23} - 638976 q^{24} - 1196225 q^{25} + 2849504 q^{26} + 2344680 q^{27} - 243712 q^{28} - 3840450 q^{29} - 2171520 q^{30} - 1309408 q^{31} + 1048576 q^{32} + 8759088 q^{33} - 3962592 q^{34} - 828240 q^{35} + 1191168 q^{36} + 4307078 q^{37} + 5046080 q^{38} - 27782664 q^{39} + 3563520 q^{40} + 1512042 q^{41} + 2376192 q^{42} + 33670604 q^{43} - 14373888 q^{44} + 4048110 q^{45} + 3272064 q^{46} - 10581072 q^{47} - 10223616 q^{48} - 39447303 q^{49} - 19139600 q^{50} + 38635272 q^{51} + 45592064 q^{52} + 16616214 q^{53} + 37514880 q^{54} - 48848760 q^{55} - 3899392 q^{56} - 49199280 q^{57} - 61447200 q^{58} + 112235100 q^{59} - 34744320 q^{60} - 33197218 q^{61} - 20950528 q^{62} - 4429656 q^{63} + 16777216 q^{64} + 154941780 q^{65} + 140145408 q^{66} - 121372252 q^{67} - 63401472 q^{68} - 31902624 q^{69} - 13251840 q^{70} - 387172728 q^{71} + 19058688 q^{72} + 255240074 q^{73} + 68913248 q^{74} + 186611100 q^{75} + 80737280 q^{76} + 53452896 q^{77} - 444522624 q^{78} + 492101840 q^{79} + 57016320 q^{80} - 457355079 q^{81} + 24192672 q^{82} - 457420236 q^{83} + 38019072 q^{84} - 215465940 q^{85} + 538729664 q^{86} + 599110200 q^{87} - 229982208 q^{88} - 31809510 q^{89} + 64769760 q^{90} - 169545488 q^{91} + 52353024 q^{92} + 204267648 q^{93} - 169297152 q^{94} + 274380600 q^{95} - 163577856 q^{96} - 673532062 q^{97} - 631156848 q^{98} - 261256644 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2.10.a \(\chi_{2}(1, \cdot)\) 2.10.a.a 1 1