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Properties

Label 10.8
Level 10
Weight 8
Dimension 5
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 10 = 2 \cdot 5 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(10))\).

Total New Old
Modular forms 25 5 20
Cusp forms 17 5 12
Eisenstein series 8 0 8

Trace form

\( 5 q + 8 q^{2} + 28 q^{3} - 192 q^{4} + 185 q^{5} + 1120 q^{6} + 104 q^{7} + 512 q^{8} - 8191 q^{9} + O(q^{10}) \) \( 5 q + 8 q^{2} + 28 q^{3} - 192 q^{4} + 185 q^{5} + 1120 q^{6} + 104 q^{7} + 512 q^{8} - 8191 q^{9} + 360 q^{10} + 12660 q^{11} + 1792 q^{12} - 8602 q^{13} - 5696 q^{14} - 31460 q^{15} + 20480 q^{16} + 20274 q^{17} - 11224 q^{18} + 109100 q^{19} + 4160 q^{20} - 61040 q^{21} - 41184 q^{22} - 72072 q^{23} - 43008 q^{24} + 101725 q^{25} - 124880 q^{26} - 100520 q^{27} + 6656 q^{28} + 401070 q^{29} + 438240 q^{30} - 474240 q^{31} + 32768 q^{32} - 144144 q^{33} - 536176 q^{34} - 263720 q^{35} + 344640 q^{36} + 104654 q^{37} + 364000 q^{38} + 922568 q^{39} + 104960 q^{40} + 817410 q^{41} + 23296 q^{42} - 795532 q^{43} - 1469184 q^{44} - 3054795 q^{45} + 569920 q^{46} + 425664 q^{47} + 114688 q^{48} + 1707381 q^{49} + 2486600 q^{50} + 928760 q^{51} - 550528 q^{52} + 1500798 q^{53} - 5920320 q^{54} - 1169980 q^{55} + 471040 q^{56} + 1274000 q^{57} + 1852080 q^{58} + 2339940 q^{59} + 2461440 q^{60} - 4357490 q^{61} - 641024 q^{62} - 145912 q^{63} - 786432 q^{64} + 1686190 q^{65} + 1248640 q^{66} - 2336836 q^{67} + 1297536 q^{68} + 4496848 q^{69} + 2783680 q^{70} - 8036040 q^{71} - 718336 q^{72} - 3805702 q^{73} - 2289296 q^{74} - 6960100 q^{75} - 1158400 q^{76} - 535392 q^{77} - 1926848 q^{78} + 12780080 q^{79} + 757760 q^{80} + 16682205 q^{81} + 4679376 q^{82} - 45492 q^{83} + 4279296 q^{84} - 5461270 q^{85} - 1952480 q^{86} + 6482280 q^{87} - 2635776 q^{88} - 32490030 q^{89} - 16982520 q^{90} + 4446160 q^{91} - 4612608 q^{92} - 2243584 q^{93} + 18945664 q^{94} + 37591900 q^{95} + 4587520 q^{96} - 5247646 q^{97} - 6501816 q^{98} - 11887132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(10))\)

We only show spaces with even 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
10.8.a \(\chi_{10}(1, \cdot)\) 10.8.a.a 1 1
10.8.b \(\chi_{10}(9, \cdot)\) 10.8.b.a 4 1

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(10))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(10)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)