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Properties

Label 11.7
Level 11
Weight 7
Dimension 25
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 70
Trace bound 1

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(70\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(11))\).

Total New Old
Modular forms 35 35 0
Cusp forms 25 25 0
Eisenstein series 10 10 0

Trace form

\( 25 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} + 2075 q^{9} + O(q^{10}) \) \( 25 q - 5 q^{2} - 5 q^{3} - 5 q^{4} - 5 q^{5} - 405 q^{6} - 365 q^{7} + 1595 q^{8} + 2075 q^{9} - 1605 q^{11} - 10250 q^{12} - 1805 q^{13} + 10650 q^{14} - 1345 q^{15} - 6305 q^{16} + 3635 q^{17} + 11970 q^{18} + 23845 q^{19} + 28340 q^{20} - 40955 q^{22} + 6610 q^{23} - 123775 q^{24} - 86165 q^{25} - 57030 q^{26} + 44845 q^{27} + 226540 q^{28} + 134595 q^{29} + 220420 q^{30} - 20705 q^{31} - 68355 q^{33} - 295270 q^{34} - 377445 q^{35} - 476010 q^{36} - 42605 q^{37} + 116540 q^{38} + 443075 q^{39} + 704340 q^{40} + 490975 q^{41} + 804110 q^{42} - 771560 q^{44} - 1073590 q^{45} - 714610 q^{46} - 329325 q^{47} - 462120 q^{48} + 106255 q^{49} + 417855 q^{50} + 1169565 q^{51} + 1468510 q^{52} + 350235 q^{53} - 313565 q^{55} - 1690380 q^{56} - 1435995 q^{57} - 1385540 q^{58} + 293425 q^{59} + 1224460 q^{60} + 892675 q^{61} + 2337360 q^{62} + 900840 q^{63} + 1125495 q^{64} - 1154250 q^{66} - 507610 q^{67} - 1822680 q^{68} - 1491530 q^{69} - 2213340 q^{70} + 650795 q^{71} + 954565 q^{72} - 806585 q^{73} - 404170 q^{74} - 925935 q^{75} + 1631815 q^{77} + 2235280 q^{78} + 1662955 q^{79} + 2028100 q^{80} + 972005 q^{81} - 618695 q^{82} + 14645 q^{83} - 2604390 q^{84} - 33365 q^{85} - 1239325 q^{86} - 395285 q^{88} + 12690 q^{89} + 4118080 q^{90} + 935815 q^{91} + 3592540 q^{92} - 5126685 q^{93} - 5913080 q^{94} - 4329525 q^{95} - 6429020 q^{96} - 1533395 q^{97} + 2872175 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(11))\)

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
11.7.b \(\chi_{11}(10, \cdot)\) 11.7.b.a 1 1
11.7.b.b 4
11.7.d \(\chi_{11}(2, \cdot)\) 11.7.d.a 20 4