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Properties

Label 4.11
Level 4
Weight 11
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 11
Trace bound 0

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Defining parameters

Level: \( N \) = \( 4 = 2^{2} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(4))\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9} + O(q^{10}) \) \( 4 q - 12 q^{2} + 16 q^{4} - 1560 q^{5} + 7200 q^{6} - 36288 q^{8} - 28764 q^{9} + 263240 q^{10} - 915840 q^{12} + 212264 q^{13} + 1901760 q^{14} - 3612416 q^{16} - 171384 q^{17} + 4740372 q^{18} - 3108960 q^{20} - 483840 q^{21} - 1996320 q^{22} + 17902080 q^{24} - 5358420 q^{25} - 32439672 q^{26} + 36099840 q^{28} + 30046632 q^{29} - 58656960 q^{30} + 58057728 q^{32} - 65537280 q^{33} - 9311128 q^{34} - 55964016 q^{36} + 134408936 q^{37} + 150268320 q^{38} - 229928320 q^{40} - 340180152 q^{41} + 327237120 q^{42} - 302075520 q^{44} + 606940200 q^{45} + 241181760 q^{46} - 244684800 q^{48} - 804921404 q^{49} - 185601540 q^{50} + 382483616 q^{52} + 1437571944 q^{53} - 631903680 q^{54} + 1392491520 q^{56} - 2610835200 q^{57} - 1349585656 q^{58} + 1623087360 q^{60} + 3412083368 q^{61} - 1633009920 q^{62} - 36368384 q^{64} - 4153551600 q^{65} + 713214720 q^{66} + 117217824 q^{68} + 4399188480 q^{69} + 2298979200 q^{70} - 4132504512 q^{72} - 2988510136 q^{73} + 1718257992 q^{74} - 7437974400 q^{76} + 3748200960 q^{77} + 7251497280 q^{78} + 1359198720 q^{80} - 4715780796 q^{81} + 6420307496 q^{82} - 3911362560 q^{84} - 1190796080 q^{85} - 8760249120 q^{86} + 1708439040 q^{88} + 5274721992 q^{89} - 5495216760 q^{90} + 22420389120 q^{92} - 6070118400 q^{93} - 7391671680 q^{94} + 5494579200 q^{96} + 14343199496 q^{97} - 30380986188 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(4))\)

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
4.11.b \(\chi_{4}(3, \cdot)\) 4.11.b.a 4 1