Properties

Label 12.12
Level 12
Weight 12
Dimension 22
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)

Dimensions

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

Total New Old
Modular forms 49 26 23
Cusp forms 39 22 17
Eisenstein series 10 4 6

Trace form

\( 22 q + 1976 q^{4} + 12852 q^{5} + 13128 q^{6} - 77000 q^{7} + 221718 q^{9} + O(q^{10}) \) \( 22 q + 1976 q^{4} + 12852 q^{5} + 13128 q^{6} - 77000 q^{7} + 221718 q^{9} + 202000 q^{10} - 137808 q^{11} + 1064760 q^{12} + 2636564 q^{13} - 1732104 q^{15} + 3482912 q^{16} - 2702700 q^{17} + 2557392 q^{18} + 170800 q^{19} + 10935456 q^{21} - 5920464 q^{22} - 25261200 q^{23} + 12133152 q^{24} - 130793806 q^{25} - 3604848 q^{28} - 226450188 q^{29} + 73456080 q^{30} + 374152408 q^{31} + 588000360 q^{33} + 222167104 q^{34} - 834294384 q^{35} + 298087896 q^{36} - 179754700 q^{37} + 732207600 q^{39} - 439643840 q^{40} - 1031482620 q^{41} + 281776944 q^{42} + 1563677200 q^{43} + 1779125268 q^{45} - 2392795680 q^{46} - 4139780400 q^{47} + 689090592 q^{48} + 2528561198 q^{49} + 1436386608 q^{51} - 3959246384 q^{52} - 2251057500 q^{53} - 4249352520 q^{54} - 6139603008 q^{55} + 1285108992 q^{57} + 9671853040 q^{58} + 14284492992 q^{59} + 5688375360 q^{60} + 6173174468 q^{61} - 4546773000 q^{63} - 1452752512 q^{64} - 3717354600 q^{65} - 10961242896 q^{66} - 1966587200 q^{67} - 28074185184 q^{69} + 35188514400 q^{70} + 25293783600 q^{71} + 30438127680 q^{72} - 26204404612 q^{73} - 22261000608 q^{75} - 60088673808 q^{76} + 75518805600 q^{77} - 81037845456 q^{78} - 35976619976 q^{79} - 35489305962 q^{81} + 88180337440 q^{82} - 3501565200 q^{83} + 125502443664 q^{84} - 21299051704 q^{85} - 13860768600 q^{87} - 166086469440 q^{88} - 55164907980 q^{89} - 257976145200 q^{90} + 101443739600 q^{91} + 136814325456 q^{93} + 391966360512 q^{94} + 3349296000 q^{95} + 446868262272 q^{96} + 169163551628 q^{97} - 8137424592 q^{99} + O(q^{100}) \)

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

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
12.12.a \(\chi_{12}(1, \cdot)\) 12.12.a.a 1 1
12.12.a.b 1
12.12.b \(\chi_{12}(11, \cdot)\) 12.12.b.a 20 1

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

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