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Properties

Label 7.7
Level 7
Weight 7
Dimension 9
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 28
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(28\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 15 15 0
Cusp forms 9 9 0
Eisenstein series 6 6 0

Trace form

\( 9 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 165 q^{5} - 483 q^{7} - 711 q^{8} - 1851 q^{9} + O(q^{10}) \) \( 9 q - 3 q^{2} - 3 q^{3} - 3 q^{4} + 165 q^{5} - 483 q^{7} - 711 q^{8} - 1851 q^{9} + 2580 q^{10} + 4113 q^{11} + 5964 q^{12} - 11151 q^{14} - 16830 q^{15} - 10023 q^{16} + 8229 q^{17} + 34209 q^{18} + 29985 q^{19} - 37527 q^{21} - 59910 q^{22} - 4875 q^{23} + 28872 q^{24} + 62745 q^{25} + 33768 q^{26} - 23835 q^{28} - 25518 q^{29} - 43200 q^{30} - 39399 q^{31} - 56055 q^{32} - 36711 q^{33} + 74865 q^{35} + 187881 q^{36} + 124905 q^{37} + 60960 q^{38} - 183372 q^{39} - 137280 q^{40} + 206136 q^{42} + 221610 q^{43} - 89298 q^{44} - 370530 q^{45} - 465006 q^{46} - 407823 q^{47} + 328545 q^{49} + 502065 q^{50} + 603369 q^{51} + 128856 q^{52} + 62577 q^{53} - 44496 q^{54} + 66801 q^{56} - 423054 q^{57} - 381030 q^{58} - 436299 q^{59} - 207900 q^{60} + 141201 q^{61} - 217875 q^{63} - 93999 q^{64} + 210420 q^{65} + 1025532 q^{66} + 1637829 q^{67} + 799596 q^{68} - 1863120 q^{70} - 1888974 q^{71} - 1509759 q^{72} - 421599 q^{73} + 173814 q^{74} + 826050 q^{75} + 709485 q^{77} + 330624 q^{78} + 433269 q^{79} + 2654040 q^{80} + 1867068 q^{81} + 2585016 q^{82} - 1982148 q^{84} - 2215950 q^{85} - 2589894 q^{86} - 1909746 q^{87} - 491598 q^{88} - 2990823 q^{89} - 687960 q^{91} + 791898 q^{92} + 3031977 q^{93} + 223584 q^{94} + 1240005 q^{95} + 972720 q^{96} + 3425541 q^{98} + 1018098 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
7.7.b \(\chi_{7}(6, \cdot)\) 7.7.b.a 1 1
7.7.b.b 2
7.7.d \(\chi_{7}(3, \cdot)\) 7.7.d.a 2 2
7.7.d.b 4