Properties

Label 8.10
Level 8
Weight 10
Dimension 10
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 40
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 21 12 9
Cusp forms 15 10 5
Eisenstein series 6 2 4

Trace form

\( 10q - 18q^{2} + 8q^{3} - 428q^{4} - 564q^{5} + 4684q^{6} + 10704q^{7} - 3384q^{8} - 70510q^{9} + O(q^{10}) \) \( 10q - 18q^{2} + 8q^{3} - 428q^{4} - 564q^{5} + 4684q^{6} + 10704q^{7} - 3384q^{8} - 70510q^{9} + 26392q^{10} + 97560q^{11} + 54760q^{12} - 188836q^{13} - 72336q^{14} + 63984q^{15} + 185616q^{16} - 273228q^{17} - 23614q^{18} - 53720q^{19} + 1245264q^{20} + 957504q^{21} - 2373124q^{22} + 809328q^{23} - 3961456q^{24} + 251942q^{25} + 4551240q^{26} - 216496q^{27} + 7509920q^{28} + 1154940q^{29} - 15284368q^{30} - 4237504q^{31} - 14113248q^{32} - 5294080q^{33} + 27757244q^{34} + 24483936q^{35} + 57226188q^{36} - 13132788q^{37} - 63661140q^{38} - 28864080q^{39} - 93063648q^{40} - 17247708q^{41} + 127541344q^{42} + 45379928q^{43} + 114013320q^{44} + 10617052q^{45} - 131840944q^{46} - 71842080q^{47} - 217917408q^{48} + 67621306q^{49} + 231784902q^{50} + 29265040q^{51} + 219270896q^{52} + 39751980q^{53} - 362934280q^{54} - 181247664q^{55} - 358503360q^{56} + 201200832q^{57} + 375425192q^{58} + 173485944q^{59} + 516952992q^{60} - 12522052q^{61} - 344291904q^{62} - 307658480q^{63} - 316815296q^{64} - 387768792q^{65} + 239713176q^{66} + 195391624q^{67} + 79875048q^{68} - 85728064q^{69} - 56202048q^{70} + 895676496q^{71} + 112273016q^{72} - 531984284q^{73} - 65773608q^{74} - 118666760q^{75} - 87532760q^{76} - 366658368q^{77} + 318117968q^{78} - 283230688q^{79} + 890441280q^{80} + 555523674q^{81} - 1051981172q^{82} - 291672408q^{83} - 1275608768q^{84} + 886884952q^{85} + 1492810428q^{86} + 353356080q^{87} + 1544767952q^{88} + 738186756q^{89} - 3218579800q^{90} - 1756556064q^{91} - 2959012128q^{92} + 479023360q^{93} + 3068552352q^{94} + 437438640q^{95} + 4296343616q^{96} + 194730196q^{97} - 3062604162q^{98} - 1565047496q^{99} + O(q^{100}) \)

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

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8.10.a \(\chi_{8}(1, \cdot)\) 8.10.a.a 1 1
8.10.a.b 1
8.10.b \(\chi_{8}(5, \cdot)\) 8.10.b.a 8 1

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

\( S_{10}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)