Properties

Label 7.5
Level 7
Weight 5
Dimension 5
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 20
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(7))\).

Total New Old
Modular forms 11 11 0
Cusp forms 5 5 0
Eisenstein series 6 6 0

Trace form

\( 5q - 3q^{2} + 6q^{3} - 35q^{4} - 30q^{5} + 49q^{7} + 273q^{8} + 57q^{9} + O(q^{10}) \) \( 5q - 3q^{2} + 6q^{3} - 35q^{4} - 30q^{5} + 49q^{7} + 273q^{8} + 57q^{9} - 204q^{10} - 264q^{11} - 588q^{12} + 609q^{14} + 468q^{15} + 137q^{16} - 246q^{17} + 297q^{18} + 642q^{19} - 1050q^{21} - 1470q^{22} - 444q^{23} + 720q^{24} + 53q^{25} + 1008q^{26} - 763q^{28} - 942q^{29} - 72q^{30} + 3618q^{31} + 2289q^{32} + 2070q^{33} - 2478q^{35} - 2847q^{36} - 1564q^{37} - 6168q^{38} - 1428q^{39} - 1752q^{40} + 6048q^{42} + 2138q^{43} + 5502q^{44} + 1944q^{45} + 1650q^{46} - 1542q^{47} + 1421q^{49} + 8193q^{50} - 4734q^{51} - 3192q^{52} - 10092q^{53} - 11016q^{54} - 2751q^{56} + 11052q^{57} + 330q^{58} + 2526q^{59} - 756q^{60} - 282q^{61} + 3633q^{63} - 8111q^{64} + 5796q^{65} - 2556q^{66} + 3628q^{67} + 20412q^{68} + 3360q^{70} - 7494q^{71} - 3807q^{72} + 5214q^{73} + 2742q^{74} - 9636q^{75} - 18984q^{77} - 9072q^{78} - 11756q^{79} - 3144q^{80} + 15867q^{81} - 4032q^{82} + 588q^{84} - 15492q^{85} + 12594q^{86} + 5976q^{87} + 3474q^{88} + 33990q^{89} + 17640q^{91} - 9222q^{92} + 7446q^{93} + 27768q^{94} + 6558q^{95} - 35427q^{98} - 6318q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
7.5.b \(\chi_{7}(6, \cdot)\) 7.5.b.a 1 1
7.5.d \(\chi_{7}(3, \cdot)\) 7.5.d.a 4 2