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Properties

Label 6.12
Level 6
Weight 12
Dimension 3
Nonzero newspaces 1
Newform subspaces 3
Sturm bound 24
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 3 \)
Sturm bound: \(24\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(6))\).

Total New Old
Modular forms 13 3 10
Cusp forms 9 3 6
Eisenstein series 4 0 4

Trace form

\( 3 q - 32 q^{2} + 243 q^{3} + 3072 q^{4} - 2334 q^{5} + 7776 q^{6} + 55392 q^{7} - 32768 q^{8} + 177147 q^{9} + O(q^{10}) \) \( 3 q - 32 q^{2} + 243 q^{3} + 3072 q^{4} - 2334 q^{5} + 7776 q^{6} + 55392 q^{7} - 32768 q^{8} + 177147 q^{9} + 307008 q^{10} - 1699116 q^{11} + 248832 q^{12} + 217266 q^{13} + 335360 q^{14} - 3369438 q^{15} + 3145728 q^{16} + 8603622 q^{17} - 1889568 q^{18} + 7200204 q^{19} - 2390016 q^{20} - 21757248 q^{21} + 5811840 q^{22} - 1057800 q^{23} + 7962624 q^{24} + 37532181 q^{25} - 165855424 q^{26} + 14348907 q^{27} + 56721408 q^{28} + 70389066 q^{29} + 164275776 q^{30} - 146569368 q^{31} - 33554432 q^{32} - 214136460 q^{33} + 255268800 q^{34} + 1123978944 q^{35} + 181398528 q^{36} - 1480918566 q^{37} - 925913728 q^{38} - 611837550 q^{39} + 314376192 q^{40} + 899560158 q^{41} + 1208452608 q^{42} - 273486252 q^{43} - 1739894784 q^{44} - 137820366 q^{45} + 1348363008 q^{46} + 1552169280 q^{47} + 254803968 q^{48} + 2904631227 q^{49} - 3482708192 q^{50} - 544856058 q^{51} + 222480384 q^{52} - 1324585278 q^{53} + 459165024 q^{54} + 1121307192 q^{55} + 343408640 q^{56} - 5621075028 q^{57} - 408318912 q^{58} + 4411180500 q^{59} - 3450304512 q^{60} - 12529017966 q^{61} + 14322308864 q^{62} + 3270842208 q^{63} + 3221225472 q^{64} - 16758434292 q^{65} - 4947682176 q^{66} + 27115273932 q^{67} + 8810108928 q^{68} + 25109273592 q^{69} - 28315634688 q^{70} - 25932460536 q^{71} - 1934917632 q^{72} + 6082420686 q^{73} + 26916324416 q^{74} + 16692865317 q^{75} + 7373008896 q^{76} - 28048880640 q^{77} - 19034606016 q^{78} - 58308979368 q^{79} - 2447376384 q^{80} + 10460353203 q^{81} - 52338500928 q^{82} + 37956458316 q^{83} - 22279421952 q^{84} + 121299146244 q^{85} + 48461612672 q^{86} - 40525895862 q^{87} + 5951324160 q^{88} - 210662658 q^{89} + 18128515392 q^{90} - 49315648704 q^{91} - 1083187200 q^{92} - 7597286136 q^{93} + 127169639424 q^{94} + 13965964680 q^{95} + 8153726976 q^{96} - 49488374586 q^{97} - 150071184672 q^{98} - 100331100684 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.12.a \(\chi_{6}(1, \cdot)\) 6.12.a.a 1 1
6.12.a.b 1
6.12.a.c 1

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

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