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Properties

Label 24.10
Level 24
Weight 10
Dimension 57
Nonzero newspaces 3
Newform subspaces 7
Sturm bound 320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 7 \)
Sturm bound: \(320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(24))\).

Total New Old
Modular forms 156 61 95
Cusp forms 132 57 75
Eisenstein series 24 4 20

Trace form

\( 57 q + 34 q^{2} - 83 q^{3} + 852 q^{4} - 122 q^{5} - 3662 q^{6} - 15508 q^{7} + 15844 q^{8} - 85295 q^{9} + O(q^{10}) \) \( 57 q + 34 q^{2} - 83 q^{3} + 852 q^{4} - 122 q^{5} - 3662 q^{6} - 15508 q^{7} + 15844 q^{8} - 85295 q^{9} - 41340 q^{10} - 56924 q^{11} + 568 q^{12} + 253814 q^{13} - 209204 q^{14} + 183222 q^{15} + 820256 q^{16} + 575686 q^{17} - 1542506 q^{18} - 314592 q^{19} + 406744 q^{20} - 120528 q^{21} + 3129696 q^{22} - 1072416 q^{23} + 768676 q^{24} + 5111811 q^{25} - 7786712 q^{26} - 6856487 q^{27} + 115312 q^{28} - 736818 q^{29} - 5734812 q^{30} + 4793788 q^{31} + 19090184 q^{32} + 467252 q^{33} - 30146516 q^{34} - 32502624 q^{35} - 11315684 q^{36} + 21407934 q^{37} + 81529688 q^{38} - 30218022 q^{39} + 91891496 q^{40} - 128282 q^{41} - 35682780 q^{42} + 15051088 q^{43} - 113955840 q^{44} - 800442 q^{45} + 164287112 q^{46} - 34564728 q^{47} + 56548792 q^{48} + 20024597 q^{49} - 240578846 q^{50} + 55196078 q^{51} - 338120656 q^{52} - 122788058 q^{53} + 87176206 q^{54} + 114813304 q^{55} + 349245496 q^{56} - 11325160 q^{57} - 331799948 q^{58} + 35469124 q^{59} - 143240592 q^{60} + 203888918 q^{61} + 243931700 q^{62} + 24275700 q^{63} + 625917552 q^{64} + 103520132 q^{65} - 33829144 q^{66} - 586302888 q^{67} - 147591168 q^{68} + 163576584 q^{69} - 344503592 q^{70} - 74580352 q^{71} + 79195756 q^{72} + 1355207498 q^{73} - 478971056 q^{74} - 952661957 q^{75} + 1431740520 q^{76} - 1124684736 q^{77} - 813575544 q^{78} - 216472964 q^{79} - 666994944 q^{80} + 848752489 q^{81} + 394714884 q^{82} + 1832558108 q^{83} + 252918456 q^{84} - 291062708 q^{85} - 1435000280 q^{86} - 1525415490 q^{87} - 835557840 q^{88} - 2453796434 q^{89} - 603303444 q^{90} + 899711136 q^{91} + 4261704192 q^{92} + 1493236296 q^{93} - 2736616056 q^{94} + 2354191864 q^{95} - 2186239400 q^{96} + 1122133394 q^{97} + 4005878682 q^{98} + 1179775124 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)

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
24.10.a \(\chi_{24}(1, \cdot)\) 24.10.a.a 1 1
24.10.a.b 1
24.10.a.c 1
24.10.a.d 2
24.10.c \(\chi_{24}(23, \cdot)\) None 0 1
24.10.d \(\chi_{24}(13, \cdot)\) 24.10.d.a 18 1
24.10.f \(\chi_{24}(11, \cdot)\) 24.10.f.a 2 1
24.10.f.b 32

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(24))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(24)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 1}\)