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Properties

Label 17.6
Level 17
Weight 6
Dimension 52
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 144
Trace bound 3

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(144\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(17))\).

Total New Old
Modular forms 68 66 2
Cusp forms 52 52 0
Eisenstein series 16 14 2

Trace form

\( 52 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 52 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9} - 1272 q^{10} + 624 q^{11} + 4216 q^{12} + 800 q^{13} - 712 q^{14} - 4352 q^{15} - 7184 q^{16} - 1920 q^{17} - 3984 q^{18} + 560 q^{19} + 8504 q^{20} + 12208 q^{21} + 9528 q^{22} + 3600 q^{23} - 22424 q^{24} - 7316 q^{25} + 12328 q^{26} + 21376 q^{27} + 33160 q^{28} + 5892 q^{29} - 10952 q^{30} - 19368 q^{31} - 37424 q^{32} - 34864 q^{33} - 67528 q^{34} - 26288 q^{35} - 26184 q^{36} + 4824 q^{37} - 14880 q^{38} + 12552 q^{39} + 133048 q^{40} + 83196 q^{41} + 196072 q^{42} + 58352 q^{43} + 77912 q^{44} - 43228 q^{45} - 122936 q^{46} - 40848 q^{47} - 141472 q^{48} - 72168 q^{49} - 140016 q^{50} - 78376 q^{51} - 134160 q^{52} - 167428 q^{53} - 198392 q^{54} + 15160 q^{55} + 231312 q^{56} + 324808 q^{57} + 351088 q^{58} + 257464 q^{59} + 574768 q^{60} + 135896 q^{61} + 115920 q^{62} - 129440 q^{63} - 281912 q^{64} - 383268 q^{65} - 586432 q^{66} - 143664 q^{67} - 604288 q^{68} - 520096 q^{69} - 341264 q^{70} - 22136 q^{71} + 260304 q^{72} + 336692 q^{73} + 386104 q^{74} + 642424 q^{75} + 645408 q^{76} + 439848 q^{77} + 856064 q^{78} + 198712 q^{79} + 63256 q^{80} - 65392 q^{81} - 471376 q^{82} - 686696 q^{83} - 2097312 q^{84} - 928980 q^{85} - 201856 q^{86} - 6248 q^{87} + 169400 q^{88} + 425056 q^{89} + 1188504 q^{90} + 706568 q^{91} + 1229384 q^{92} + 563544 q^{93} + 847064 q^{94} + 341320 q^{95} + 273632 q^{96} + 198392 q^{97} - 611568 q^{98} - 893760 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.6.a \(\chi_{17}(1, \cdot)\) 17.6.a.a 1 1
17.6.a.b 1
17.6.a.c 4
17.6.b \(\chi_{17}(16, \cdot)\) 17.6.b.a 6 1
17.6.c \(\chi_{17}(4, \cdot)\) 17.6.c.a 12 2
17.6.d \(\chi_{17}(2, \cdot)\) 17.6.d.a 28 4