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Properties

Label 12.10
Level 12
Weight 10
Dimension 17
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 80
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(12))\).

Total New Old
Modular forms 41 21 20
Cusp forms 31 17 14
Eisenstein series 10 4 6

Trace form

\( 17 q - 81 q^{3} - 344 q^{4} + 990 q^{5} - 1608 q^{6} + 8576 q^{7} - 7311 q^{9} + O(q^{10}) \) \( 17 q - 81 q^{3} - 344 q^{4} + 990 q^{5} - 1608 q^{6} + 8576 q^{7} - 7311 q^{9} - 15952 q^{10} + 70596 q^{11} + 42600 q^{12} - 99842 q^{13} - 80190 q^{15} + 164896 q^{16} - 200574 q^{17} + 256944 q^{18} - 695620 q^{19} - 338208 q^{21} + 322128 q^{22} + 2472696 q^{23} + 166176 q^{24} - 3716753 q^{25} - 531441 q^{27} - 1447056 q^{28} + 5474214 q^{29} + 3286128 q^{30} + 3732104 q^{31} - 1002756 q^{33} - 13198144 q^{34} + 8490240 q^{35} - 6827448 q^{36} - 10900922 q^{37} + 204930 q^{39} + 23411264 q^{40} - 23818950 q^{41} + 23964432 q^{42} + 10612676 q^{43} + 6243486 q^{45} - 41256288 q^{46} + 2398464 q^{47} - 87722976 q^{48} + 11837545 q^{49} + 16246494 q^{51} + 132124208 q^{52} - 8994978 q^{53} + 179732232 q^{54} + 69890040 q^{55} - 32094684 q^{57} - 271309360 q^{58} - 143417916 q^{59} - 414400704 q^{60} + 30880894 q^{61} + 56267136 q^{63} + 742710400 q^{64} - 2504700 q^{65} + 790585104 q^{66} - 165625156 q^{67} - 136575096 q^{69} - 1188731232 q^{70} - 194801400 q^{71} - 1250220480 q^{72} + 172111594 q^{73} + 78815025 q^{75} + 1645242192 q^{76} + 605431296 q^{77} + 2079579408 q^{78} - 30134152 q^{79} + 392803281 q^{81} - 3274996000 q^{82} + 302054076 q^{83} - 3734920464 q^{84} - 445829444 q^{85} - 443411334 q^{87} + 4467199680 q^{88} + 909502650 q^{89} + 5726283888 q^{90} - 21697280 q^{91} - 565125672 q^{93} - 6146963136 q^{94} - 688663800 q^{95} - 6944875392 q^{96} - 841536734 q^{97} + 463180356 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.10.a \(\chi_{12}(1, \cdot)\) 12.10.a.a 1 1
12.10.b \(\chi_{12}(11, \cdot)\) 12.10.b.a 16 1

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

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