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Properties

Label 5.7
Level 5
Weight 7
Dimension 4
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 14
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} + O(q^{10}) \) \( 4 q - 10 q^{2} + 30 q^{3} - 70 q^{5} - 552 q^{6} + 550 q^{7} + 1860 q^{8} - 4370 q^{10} - 1052 q^{11} + 3480 q^{12} + 1960 q^{13} - 90 q^{15} - 776 q^{16} - 3280 q^{17} - 870 q^{18} + 20340 q^{20} + 3828 q^{21} - 27520 q^{22} - 39010 q^{23} + 30400 q^{25} + 44068 q^{26} + 31320 q^{27} - 4840 q^{28} - 50640 q^{30} - 33172 q^{31} - 48760 q^{32} + 22260 q^{33} - 24970 q^{35} - 40836 q^{36} + 146860 q^{37} + 218040 q^{38} - 110100 q^{40} - 213932 q^{41} - 31680 q^{42} - 72050 q^{43} + 78210 q^{45} + 323288 q^{46} + 830 q^{47} - 74160 q^{48} - 203350 q^{50} - 172212 q^{51} - 173300 q^{52} - 29620 q^{53} + 470660 q^{55} + 467280 q^{56} + 195840 q^{57} - 554640 q^{58} + 620280 q^{60} - 111052 q^{61} - 610520 q^{62} - 350130 q^{63} - 406540 q^{65} - 457824 q^{66} - 146930 q^{67} + 775780 q^{68} - 133320 q^{70} + 1310188 q^{71} + 899460 q^{72} + 553540 q^{73} - 435450 q^{75} - 2073840 q^{76} - 476300 q^{77} + 268200 q^{78} - 1011520 q^{80} - 624816 q^{81} + 2554880 q^{82} + 536870 q^{83} - 1344920 q^{85} + 1019128 q^{86} - 763440 q^{87} - 187680 q^{88} + 947310 q^{90} + 1131548 q^{91} - 2552680 q^{92} + 444660 q^{93} + 912600 q^{95} - 568992 q^{96} - 59420 q^{97} - 1892810 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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
5.7.c \(\chi_{5}(2, \cdot)\) 5.7.c.a 4 2