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Properties

Label 61.7
Level 61
Weight 7
Dimension 900
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 2170
Trace bound 1

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Defining parameters

Level: \( N \) = \( 61 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(2170\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(61))\).

Total New Old
Modular forms 960 960 0
Cusp forms 900 900 0
Eisenstein series 60 60 0

Trace form

\( 900 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{5} - 30 q^{6} - 30 q^{7} - 30 q^{8} - 30 q^{9} + O(q^{10}) \) \( 900 q - 30 q^{2} - 30 q^{3} - 30 q^{4} - 30 q^{5} - 30 q^{6} - 30 q^{7} - 30 q^{8} - 30 q^{9} - 30 q^{10} - 30 q^{11} - 30 q^{12} - 30 q^{13} - 30 q^{14} - 30 q^{15} - 30 q^{16} - 30 q^{17} - 30 q^{18} - 30 q^{19} - 30 q^{20} - 30 q^{21} - 30 q^{22} - 30 q^{23} - 30 q^{24} - 30 q^{25} - 30 q^{26} - 30 q^{27} - 30 q^{28} - 30 q^{29} - 30 q^{30} - 30 q^{31} - 30 q^{32} - 30 q^{33} - 30 q^{34} - 30 q^{35} - 30 q^{36} - 30 q^{37} - 30 q^{38} - 30 q^{39} - 30 q^{40} - 30 q^{41} - 30 q^{42} - 30 q^{43} - 30 q^{44} - 30 q^{45} - 30 q^{46} + 1332210 q^{47} - 30 q^{48} - 1441470 q^{49} - 1875030 q^{50} - 1166430 q^{51} - 1987230 q^{52} + 92370 q^{53} + 2449410 q^{54} + 2519970 q^{55} + 4377570 q^{56} + 2799330 q^{57} + 2203170 q^{58} + 612450 q^{59} - 1419630 q^{61} - 3800220 q^{62} - 3790830 q^{63} - 8110110 q^{64} - 2040030 q^{65} - 3499230 q^{66} - 2298270 q^{67} - 806430 q^{68} + 1632930 q^{69} + 5939970 q^{70} + 1517970 q^{71} + 13996770 q^{72} + 3743970 q^{73} + 3330570 q^{74} - 30 q^{75} - 8064030 q^{76} - 6270990 q^{77} - 30 q^{78} - 30 q^{79} - 30 q^{80} - 30 q^{81} - 30 q^{82} - 30 q^{83} - 30 q^{84} - 30 q^{85} - 30 q^{86} - 30 q^{87} - 30 q^{88} - 30 q^{89} - 30 q^{90} - 30 q^{91} - 30 q^{92} - 30 q^{93} - 30 q^{94} - 30 q^{95} - 30 q^{96} - 30 q^{97} - 30 q^{98} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(61))\)

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
61.7.d \(\chi_{61}(11, \cdot)\) 61.7.d.a 60 2
61.7.h \(\chi_{61}(21, \cdot)\) 61.7.h.a 120 4
61.7.j \(\chi_{61}(8, \cdot)\) 61.7.j.a 240 8
61.7.l \(\chi_{61}(2, \cdot)\) 61.7.l.a 480 16