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Properties

Label 59.12
Level 59
Weight 12
Dimension 1564
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 3480
Trace bound 1

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Defining parameters

Level: \( N \) = \( 59 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(3480\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(59))\).

Total New Old
Modular forms 1624 1620 4
Cusp forms 1566 1564 2
Eisenstein series 58 56 2

Trace form

\( 1564 q + 19 q^{2} - 533 q^{3} + 2915 q^{4} - 9689 q^{5} + 12067 q^{6} + 33459 q^{7} - 168989 q^{8} + 227257 q^{9} + O(q^{10}) \) \( 1564 q + 19 q^{2} - 533 q^{3} + 2915 q^{4} - 9689 q^{5} + 12067 q^{6} + 33459 q^{7} - 168989 q^{8} + 227257 q^{9} + 231811 q^{10} - 1069253 q^{11} + 741859 q^{12} + 1155447 q^{13} - 803741 q^{14} - 2434349 q^{15} - 1974301 q^{16} + 13811839 q^{17} - 5454893 q^{18} - 21322869 q^{19} + 14219491 q^{20} + 8438947 q^{21} + 25661347 q^{22} - 37286573 q^{23} - 42577949 q^{24} + 50998421 q^{25} - 27731453 q^{26} + 146558131 q^{27} - 49294365 q^{28} - 256813289 q^{29} + 58423651 q^{30} + 105686307 q^{31} + 393412579 q^{32} - 269444477 q^{33} - 331484861 q^{34} + 161747011 q^{35} - 334565021 q^{36} + 364426599 q^{37} + 511748131 q^{38} + 291179923 q^{39} - 816076829 q^{40} - 616240913 q^{41} - 202535453 q^{42} + 34251387 q^{43} + 1573897699 q^{44} - 7208882200 q^{45} + 21700130339 q^{46} - 13000128498 q^{47} - 54893402141 q^{48} + 7087031723 q^{49} + 40353380787 q^{50} + 40061926031 q^{51} - 1342964509 q^{52} - 16320568039 q^{53} - 99804206461 q^{54} - 32911655972 q^{55} + 15244607459 q^{56} + 59839428156 q^{57} + 44232210726 q^{58} + 36524005949 q^{59} + 43480132550 q^{60} - 40216607591 q^{61} - 54742799197 q^{62} - 144436023078 q^{63} - 130445123613 q^{64} + 30832678258 q^{65} + 244130472515 q^{66} + 124038039385 q^{67} + 114353000163 q^{68} - 35043477241 q^{69} - 230211912093 q^{70} - 178213977511 q^{71} - 170536184861 q^{72} + 86082627524 q^{73} + 285706625987 q^{74} - 293795612950 q^{75} + 31387220451 q^{76} + 17903086627 q^{77} - 6988318877 q^{78} - 76233691389 q^{79} - 9535733789 q^{80} - 3330376751 q^{81} + 14789781187 q^{82} + 58670199307 q^{83} - 12422172701 q^{84} + 66711322411 q^{85} - 822034013 q^{86} - 64716941549 q^{87} - 90328043549 q^{88} + 49985834191 q^{89} - 26346993149 q^{90} - 19347290173 q^{91} + 54885792739 q^{92} + 26632956643 q^{93} + 128992727779 q^{94} - 102989317229 q^{95} + 99139977187 q^{96} - 150027137121 q^{97} - 98059642646 q^{98} + 2044649364316 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(59))\)

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
59.12.a \(\chi_{59}(1, \cdot)\) 59.12.a.a 23 1
59.12.a.b 29
59.12.c \(\chi_{59}(3, \cdot)\) 59.12.c.a 1512 28

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(59))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(59)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)