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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

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

Display 100 coefficients 10 coefficients

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 available 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

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