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Properties

Label 7.11
Level 7
Weight 11
Dimension 17
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 44
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(44\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 23 23 0
Cusp forms 17 17 0
Eisenstein series 6 6 0

Trace form

\( 17 q - 3 q^{2} - 246 q^{3} - 2051 q^{4} + 3330 q^{5} - 24479 q^{7} - 39639 q^{8} + 213249 q^{9} + O(q^{10}) \) \( 17 q - 3 q^{2} - 246 q^{3} - 2051 q^{4} + 3330 q^{5} - 24479 q^{7} - 39639 q^{8} + 213249 q^{9} - 445740 q^{10} - 147768 q^{11} + 1581468 q^{12} - 1518783 q^{14} - 199980 q^{15} - 432295 q^{16} + 389178 q^{17} + 3824145 q^{18} - 5517150 q^{19} + 11878986 q^{21} - 26531958 q^{22} - 15743808 q^{23} + 31899384 q^{24} + 32924105 q^{25} + 37885176 q^{26} - 113031835 q^{28} - 51341382 q^{29} - 1661760 q^{30} - 44673798 q^{31} + 234297945 q^{32} + 293090418 q^{33} - 343947870 q^{35} - 753646503 q^{36} - 151572592 q^{37} + 528863040 q^{38} + 534862776 q^{39} + 840782640 q^{40} - 722280888 q^{42} - 968039878 q^{43} - 1137137106 q^{44} + 960213420 q^{45} + 2020314882 q^{46} + 782650314 q^{47} - 1239458479 q^{49} - 3153091215 q^{50} - 864693342 q^{51} + 1019252472 q^{52} + 1877810160 q^{53} + 4229214768 q^{54} - 4460272719 q^{56} - 2812994748 q^{57} + 1171629978 q^{58} + 456895242 q^{59} + 2488498740 q^{60} + 1469956122 q^{61} - 104452887 q^{63} - 1569252047 q^{64} - 962430840 q^{65} - 875442996 q^{66} + 1714140976 q^{67} - 3587950548 q^{68} + 7498706880 q^{70} + 7297844658 q^{71} - 695209311 q^{72} - 3308125038 q^{73} - 16641297066 q^{74} - 13137007020 q^{75} + 8289837528 q^{77} + 21758109408 q^{78} + 8712052192 q^{79} + 1013632920 q^{80} - 11533623705 q^{81} - 22926766968 q^{82} + 27068587644 q^{84} + 15369639540 q^{85} + 5072963946 q^{86} - 31859197092 q^{87} - 36466841934 q^{88} - 2675986686 q^{89} + 21332581200 q^{91} + 68900527386 q^{92} + 35364104634 q^{93} - 26955870432 q^{94} - 35799994350 q^{95} - 30016813680 q^{96} - 20652852171 q^{98} - 372627270 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
7.11.b \(\chi_{7}(6, \cdot)\) 7.11.b.a 1 1
7.11.b.b 4
7.11.d \(\chi_{7}(3, \cdot)\) 7.11.d.a 12 2