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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

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

Display 100 coefficients 10 coefficients

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 available 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

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