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Properties

Label 60.12
Level 60
Weight 12
Dimension 410
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 2304
Trace bound 1

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Defining parameters

Level: \( N \) = \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(2304\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(60))\).

Total New Old
Modular forms 1096 418 678
Cusp forms 1016 410 606
Eisenstein series 80 8 72

Trace form

\( 410 q + 506 q^{3} - 3960 q^{4} + 10210 q^{5} - 3904 q^{6} + 14252 q^{7} - 149676 q^{8} - 325346 q^{9} + O(q^{10}) \) \( 410 q + 506 q^{3} - 3960 q^{4} + 10210 q^{5} - 3904 q^{6} + 14252 q^{7} - 149676 q^{8} - 325346 q^{9} - 485380 q^{10} - 1040872 q^{11} - 1306724 q^{12} - 1624904 q^{13} + 1221530 q^{15} + 12936256 q^{16} - 30368860 q^{17} - 12252608 q^{18} - 2453600 q^{19} - 21379580 q^{20} - 75700964 q^{21} + 110297272 q^{22} + 30428640 q^{23} - 263834280 q^{24} - 700194358 q^{25} + 117902576 q^{26} + 37434038 q^{27} - 49780776 q^{28} + 435216588 q^{29} - 107697764 q^{30} - 729364952 q^{31} - 421305260 q^{32} - 975683468 q^{33} - 703535784 q^{34} - 25930240 q^{35} - 1383494992 q^{36} + 1414285888 q^{37} + 507780368 q^{38} - 1464415200 q^{39} - 4405811344 q^{40} + 2345561596 q^{41} + 5525967624 q^{42} + 191576164 q^{43} - 2724246850 q^{45} - 10349413624 q^{46} + 4003077600 q^{47} - 1760700084 q^{48} + 4101568086 q^{49} + 17271459184 q^{50} - 4753040348 q^{51} - 15202442312 q^{52} - 1610478148 q^{53} - 11293943216 q^{54} - 8021217640 q^{55} + 27643487296 q^{56} + 2866097084 q^{57} - 27408996712 q^{58} - 10975095592 q^{59} + 12154494976 q^{60} - 18372324372 q^{61} + 2762122808 q^{62} + 9222459944 q^{63} - 47978325432 q^{64} - 71008143380 q^{65} + 37605289568 q^{66} + 44196382412 q^{67} + 59989765072 q^{68} - 11496179600 q^{69} - 26770882808 q^{70} - 21162074400 q^{71} - 109564472532 q^{72} + 7708229344 q^{73} - 757186790 q^{75} + 214806636928 q^{76} - 77727400464 q^{77} + 103691781328 q^{78} + 146998674376 q^{79} - 26624754076 q^{80} - 388166731710 q^{81} - 376988340248 q^{82} - 120443873760 q^{83} + 77610672728 q^{84} + 6749629000 q^{85} + 457820899904 q^{86} + 65878849700 q^{87} - 358268451032 q^{88} + 272866724980 q^{89} - 234783302340 q^{90} - 66442140136 q^{91} + 504169750072 q^{92} - 279815134520 q^{93} + 35354855880 q^{94} - 367038432000 q^{95} - 825876822400 q^{96} - 261419682192 q^{97} + 40881015912 q^{98} + 131986797192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(60))\)

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
60.12.a \(\chi_{60}(1, \cdot)\) 60.12.a.a 2 1
60.12.a.b 2
60.12.a.c 2
60.12.a.d 2
60.12.d \(\chi_{60}(49, \cdot)\) 60.12.d.a 10 1
60.12.e \(\chi_{60}(11, \cdot)\) 60.12.e.a 88 1
60.12.h \(\chi_{60}(59, \cdot)\) 60.12.h.a 4 1
60.12.h.b 4
60.12.h.c 120
60.12.i \(\chi_{60}(17, \cdot)\) 60.12.i.a 44 2
60.12.j \(\chi_{60}(7, \cdot)\) 60.12.j.a 132 2

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(60))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(60)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 1}\)