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Properties

Label 12.15
Level 12
Weight 15
Dimension 19
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 120
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 15 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(120\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(\Gamma_1(12))\).

Total New Old
Modular forms 61 19 42
Cusp forms 51 19 32
Eisenstein series 10 0 10

Trace form

\( 19 q + 182 q^{2} - 39 q^{3} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 320266 q^{7} + 4352816 q^{8} - 23274477 q^{9} + O(q^{10}) \) \( 19 q + 182 q^{2} - 39 q^{3} + 9308 q^{4} - 16124 q^{5} + 56862 q^{6} + 320266 q^{7} + 4352816 q^{8} - 23274477 q^{9} + 586324 q^{10} + 621108 q^{12} + 104501054 q^{13} - 200755992 q^{14} + 24235200 q^{15} + 380631536 q^{16} - 291483380 q^{17} - 290166786 q^{18} + 163328530 q^{19} + 5316726088 q^{20} - 1652623206 q^{21} - 9373833288 q^{22} + 2880331488 q^{24} + 14566610183 q^{25} - 45510637748 q^{26} - 3078602991 q^{27} + 83579713776 q^{28} - 12126204812 q^{29} - 44941179132 q^{30} + 23570920570 q^{31} + 67974212192 q^{32} - 95034547944 q^{33} - 57269346212 q^{34} - 14839958484 q^{36} + 308612848478 q^{37} + 102957884712 q^{38} - 289528247670 q^{39} - 491601579872 q^{40} + 189318893932 q^{41} + 240539889384 q^{42} + 774500266114 q^{43} - 997611383472 q^{44} - 1249951379148 q^{45} + 1368039641184 q^{46} - 465649986384 q^{48} + 2136952347725 q^{49} + 2170057449522 q^{50} - 4102471929600 q^{51} - 2399333559176 q^{52} + 1251391890964 q^{53} - 90656394426 q^{54} + 7505039836800 q^{55} + 2319191796096 q^{56} - 7482316824222 q^{57} - 5157502168892 q^{58} + 2354207329944 q^{60} + 6340490433710 q^{61} - 9161379391272 q^{62} - 18741057723846 q^{63} + 17520900128384 q^{64} + 5858206778312 q^{65} - 6614704234440 q^{66} + 26321765447986 q^{67} + 18747786717976 q^{68} - 41645885250528 q^{69} - 8213486211792 q^{70} - 6939794663568 q^{72} + 69184912441910 q^{73} - 7698562888484 q^{74} - 26609974859775 q^{75} - 9224963770896 q^{76} - 41289727781472 q^{77} + 10470873014172 q^{78} + 8579718841690 q^{79} - 57127847610848 q^{80} + 34570860274611 q^{81} + 107070799921084 q^{82} - 28102976768880 q^{84} - 217249910769880 q^{85} + 102443851819896 q^{86} + 58743848116800 q^{87} - 83262676567680 q^{88} + 223721333984572 q^{89} - 934789838652 q^{90} - 124461505562620 q^{91} - 79895035003584 q^{92} + 193432896282234 q^{93} - 52692266305296 q^{94} - 2264434006752 q^{96} - 30375033666778 q^{97} - 228639957171082 q^{98} + 325346192265600 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{15}^{\mathrm{new}}(\Gamma_1(12))\)

We only show spaces with odd 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
12.15.c \(\chi_{12}(5, \cdot)\) 12.15.c.a 1 1
12.15.c.b 4
12.15.d \(\chi_{12}(7, \cdot)\) 12.15.d.a 14 1

Decomposition of \(S_{15}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{15}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{15}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{15}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)