Properties

Label 69.8
Level 69
Weight 8
Dimension 900
Nonzero newspaces 4
Newform subspaces 9
Sturm bound 2816
Trace bound 1

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Defining parameters

Level: \( N \) = \( 69 = 3 \cdot 23 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 9 \)
Sturm bound: \(2816\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(69))\).

Total New Old
Modular forms 1276 944 332
Cusp forms 1188 900 288
Eisenstein series 88 44 44

Trace form

\( 900q - 12q^{2} + 43q^{3} + 162q^{4} - 780q^{5} + 313q^{6} + 106q^{7} + 2640q^{8} - 1469q^{9} + O(q^{10}) \) \( 900q - 12q^{2} + 43q^{3} + 162q^{4} - 780q^{5} + 313q^{6} + 106q^{7} + 2640q^{8} - 1469q^{9} - 4702q^{10} + 1896q^{11} - 4979q^{12} + 10174q^{13} + 768q^{14} + 24888q^{15} - 263990q^{16} - 36158q^{17} + 269673q^{18} + 141936q^{19} + 77392q^{20} - 225194q^{21} - 457136q^{22} - 385420q^{23} - 193798q^{24} + 236104q^{25} + 859160q^{26} + 729616q^{27} + 1097706q^{28} - 240902q^{29} - 1354515q^{30} - 508104q^{31} - 1192384q^{32} + 1164000q^{33} + 3291238q^{34} - 2496580q^{35} - 1325333q^{36} - 2347498q^{37} + 3526970q^{38} + 2503429q^{39} + 12755578q^{40} + 3198560q^{41} + 516823q^{42} - 4760182q^{43} - 11537630q^{44} - 568620q^{45} - 14845238q^{46} - 5962856q^{47} - 220435q^{48} + 8796308q^{49} + 15956050q^{50} + 7927837q^{51} + 31568486q^{52} + 5541368q^{53} - 8768085q^{54} - 8181582q^{55} - 25116850q^{56} - 6237224q^{57} - 26826812q^{58} + 1131332q^{59} - 5272621q^{60} - 601346q^{61} + 3321696q^{62} - 8929614q^{63} - 1318038q^{64} + 3976440q^{65} + 16275678q^{66} + 1014466q^{67} + 5223024q^{68} + 16102998q^{69} + 299476q^{70} - 11121264q^{71} - 2873915q^{72} - 2738186q^{73} + 47926786q^{74} - 12138830q^{75} - 55293712q^{76} - 65650808q^{77} - 87767001q^{78} - 13061070q^{79} + 6805398q^{80} + 73053347q^{81} + 81202958q^{82} + 64712080q^{83} + 124501319q^{84} + 75171718q^{85} + 40218916q^{86} - 3195347q^{87} - 54626726q^{88} - 51836952q^{89} - 145710580q^{90} - 133281040q^{91} - 145622370q^{92} - 94696378q^{93} - 84371396q^{94} + 71983278q^{95} + 83586478q^{96} + 24778372q^{97} + 20588196q^{98} + 106096783q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(69))\)

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
69.8.a \(\chi_{69}(1, \cdot)\) 69.8.a.a 5 1
69.8.a.b 6
69.8.a.c 7
69.8.a.d 8
69.8.c \(\chi_{69}(68, \cdot)\) 69.8.c.a 6 1
69.8.c.b 48
69.8.e \(\chi_{69}(4, \cdot)\) 69.8.e.a 140 10
69.8.e.b 140
69.8.g \(\chi_{69}(5, \cdot)\) 69.8.g.a 540 10

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(69))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(69)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)