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Properties

Label 17.18
Level 17
Weight 18
Dimension 194
Nonzero newspaces 4
Newform subspaces 5
Sturm bound 432
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 5 \)
Sturm bound: \(432\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(17))\).

Total New Old
Modular forms 212 208 4
Cusp forms 196 194 2
Eisenstein series 16 14 2

Trace form

\( 194 q + 1048 q^{2} + 8560 q^{3} - 295432 q^{4} + 2051692 q^{5} - 4523912 q^{6} - 6451992 q^{7} + 17571832 q^{8} + 221575006 q^{9} + O(q^{10}) \) \( 194 q + 1048 q^{2} + 8560 q^{3} - 295432 q^{4} + 2051692 q^{5} - 4523912 q^{6} - 6451992 q^{7} + 17571832 q^{8} + 221575006 q^{9} - 164156232 q^{10} + 2468696600 q^{11} + 7681308664 q^{12} - 8892861308 q^{13} + 6170755320 q^{14} + 27756097168 q^{15} - 90815201296 q^{16} + 32178185582 q^{17} + 107597634960 q^{18} - 140739842360 q^{19} + 325519373304 q^{20} + 1031527510384 q^{21} - 1616848979592 q^{22} + 424685349152 q^{23} + 1259321776744 q^{24} + 1747507478894 q^{25} - 5204371889960 q^{26} + 2158401522448 q^{27} + 9114733387656 q^{28} - 15457746339928 q^{29} + 4487829281848 q^{30} + 45371932016024 q^{31} - 20771725415728 q^{32} - 51462076761232 q^{33} - 15604274263720 q^{34} + 77381229797232 q^{35} + 108224282335416 q^{36} - 124433294772724 q^{37} - 20745415736576 q^{38} - 13353886488936 q^{39} + 747723583628728 q^{40} - 400432123458328 q^{41} - 768683931073112 q^{42} + 647235020450680 q^{43} + 840336888643672 q^{44} - 1546240787336728 q^{45} + 517200221848648 q^{46} + 899619556144848 q^{47} + 1646395733037536 q^{48} + 73378600299174 q^{49} - 1881863219540016 q^{50} - 567270296482288 q^{51} + 1713876672340976 q^{52} + 4559095379390816 q^{53} - 4523374048970264 q^{54} + 211187465139880 q^{55} - 6820478690221808 q^{56} - 6352392319340024 q^{57} + 9575177102765104 q^{58} + 7417153689600960 q^{59} - 10334188651180112 q^{60} - 9748001837807588 q^{61} - 9389782694345200 q^{62} + 18435235456327120 q^{63} + 5515870806194120 q^{64} + 13740557398322532 q^{65} - 18109093458334240 q^{66} - 23386453405780792 q^{67} - 588837243112512 q^{68} + 1990674073900832 q^{69} + 61930121659077616 q^{70} + 32194160272323448 q^{71} - 73828380710457264 q^{72} - 90458932279812080 q^{73} - 777215925065624 q^{74} + 72474035566031104 q^{75} + 90625891978148000 q^{76} + 17537516910315944 q^{77} - 174056111318446720 q^{78} - 77294853838983528 q^{79} + 34470551333729816 q^{80} + 206479194429332990 q^{81} + 186917770577938016 q^{82} - 149482390841039664 q^{83} - 356480377344984480 q^{84} - 98952817841696880 q^{85} + 317238737966125696 q^{86} + 236795606055425896 q^{87} + 7194243716217272 q^{88} - 205336225647904724 q^{89} + 202128179023665864 q^{90} + 95279741399716008 q^{91} + 142813700768203336 q^{92} - 213851224241714088 q^{93} - 234557149403165224 q^{94} - 129899956026852840 q^{95} + 318953849782252640 q^{96} + 51852778986757684 q^{97} + 453451997049577632 q^{98} + 587184259034338536 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(17))\)

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
17.18.a \(\chi_{17}(1, \cdot)\) 17.18.a.a 10 1
17.18.a.b 12
17.18.b \(\chi_{17}(16, \cdot)\) 17.18.b.a 24 1
17.18.c \(\chi_{17}(4, \cdot)\) 17.18.c.a 48 2
17.18.d \(\chi_{17}(2, \cdot)\) 17.18.d.a 100 4

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(17))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(17)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)