Properties

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

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
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

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

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 the 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