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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

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

Display 100 coefficients 10 coefficients

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 available 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