Properties

Label 8.19
Level 8
Weight 19
Dimension 17
Nonzero newspaces 1
Newform subspaces 2
Sturm bound 76
Trace bound 0

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 19 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 2 \)
Sturm bound: \(76\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{19}(\Gamma_1(8))\).

Total New Old
Modular forms 39 19 20
Cusp forms 33 17 16
Eisenstein series 6 2 4

Trace form

\( 17 q - 86 q^{2} - 2 q^{3} - 182188 q^{4} - 13676516 q^{6} + 170697016 q^{8} + 1937102443 q^{9} + O(q^{10}) \) \( 17 q - 86 q^{2} - 2 q^{3} - 182188 q^{4} - 13676516 q^{6} + 170697016 q^{8} + 1937102443 q^{9} - 1569837600 q^{10} - 2825920882 q^{11} + 3908201752 q^{12} + 26163923904 q^{14} - 123600598768 q^{16} - 56596854238 q^{17} - 851393599826 q^{18} - 498351928610 q^{19} + 1256486405760 q^{20} + 241354323772 q^{22} - 1530536810864 q^{24} - 11505811874455 q^{25} + 4184514840864 q^{26} + 14061442482460 q^{27} - 12301604294400 q^{28} - 36336510039360 q^{30} + 106297370843104 q^{32} + 256848360740 q^{33} + 19294132438996 q^{34} + 20487495736320 q^{35} + 178419368263516 q^{36} + 321929676917468 q^{38} - 519930573603840 q^{40} - 72768957557902 q^{41} - 222362598288000 q^{42} - 1539904656683378 q^{43} - 19108995818920 q^{44} + 153882272211264 q^{46} + 672697260510688 q^{48} - 1558002106222399 q^{49} + 3715016028706330 q^{50} + 2524644687218684 q^{51} - 4594372123628160 q^{52} - 2655153183920264 q^{54} + 8184134137073664 q^{56} + 8446333577835140 q^{57} - 10505700099162720 q^{58} - 9672160183976146 q^{59} + 29677718651516160 q^{60} + 6212402633091840 q^{62} - 38418486876250048 q^{64} - 21153177930524160 q^{65} - 24108111108381976 q^{66} + 111961510526896702 q^{67} - 39301886160048472 q^{68} + 4248100663257600 q^{70} + 13765906108011496 q^{72} + 52959460230476818 q^{73} + 9613779604149984 q^{74} - 396847589739235250 q^{75} - 63308333396099432 q^{76} - 93022771634070720 q^{78} + 26870186366192640 q^{80} + 237317766485662405 q^{81} + 62441253547871092 q^{82} + 513396875400956318 q^{83} + 451843591950574080 q^{84} + 757073213228925500 q^{86} - 710900698406035952 q^{88} - 396588502000066510 q^{89} - 1227675520905095520 q^{90} - 379834560933460992 q^{91} + 1413121475102841600 q^{92} + 671428514272869504 q^{94} - 368237532013701056 q^{96} - 1113827538998726462 q^{97} - 915383602322888054 q^{98} - 683413807464943174 q^{99} + O(q^{100}) \)

Decomposition of \(S_{19}^{\mathrm{new}}(\Gamma_1(8))\)

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
8.19.c \(\chi_{8}(7, \cdot)\) None 0 1
8.19.d \(\chi_{8}(3, \cdot)\) 8.19.d.a 1 1
8.19.d.b 16

Decomposition of \(S_{19}^{\mathrm{old}}(\Gamma_1(8))\) into lower level spaces

\( S_{19}^{\mathrm{old}}(\Gamma_1(8)) \cong \) \(S_{19}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{19}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 1}\)