Properties

Label 12.4
Level 12
Weight 4
Dimension 5
Nonzero newspaces 2
Newforms 2
Sturm bound 32
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(12))\).

Total New Old
Modular forms 17 9 8
Cusp forms 7 5 2
Eisenstein series 10 4 6

Trace form

\(5q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 8q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 24q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut 80q^{10} \) \(\mathstrut +\mathstrut 36q^{11} \) \(\mathstrut +\mathstrut 120q^{12} \) \(\mathstrut -\mathstrut 50q^{13} \) \(\mathstrut -\mathstrut 54q^{15} \) \(\mathstrut -\mathstrut 224q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut -\mathstrut 240q^{18} \) \(\mathstrut -\mathstrut 100q^{19} \) \(\mathstrut +\mathstrut 144q^{21} \) \(\mathstrut +\mathstrut 240q^{22} \) \(\mathstrut +\mathstrut 72q^{23} \) \(\mathstrut +\mathstrut 288q^{24} \) \(\mathstrut +\mathstrut 379q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 240q^{28} \) \(\mathstrut -\mathstrut 234q^{29} \) \(\mathstrut -\mathstrut 240q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 372q^{33} \) \(\mathstrut +\mathstrut 320q^{34} \) \(\mathstrut -\mathstrut 144q^{35} \) \(\mathstrut +\mathstrut 24q^{36} \) \(\mathstrut -\mathstrut 746q^{37} \) \(\mathstrut -\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 320q^{40} \) \(\mathstrut +\mathstrut 90q^{41} \) \(\mathstrut +\mathstrut 240q^{42} \) \(\mathstrut +\mathstrut 452q^{43} \) \(\mathstrut +\mathstrut 798q^{45} \) \(\mathstrut -\mathstrut 672q^{46} \) \(\mathstrut +\mathstrut 432q^{47} \) \(\mathstrut -\mathstrut 480q^{48} \) \(\mathstrut +\mathstrut 853q^{49} \) \(\mathstrut +\mathstrut 54q^{51} \) \(\mathstrut +\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 414q^{53} \) \(\mathstrut +\mathstrut 792q^{54} \) \(\mathstrut -\mathstrut 648q^{55} \) \(\mathstrut -\mathstrut 1380q^{57} \) \(\mathstrut -\mathstrut 1360q^{58} \) \(\mathstrut -\mathstrut 684q^{59} \) \(\mathstrut -\mathstrut 960q^{60} \) \(\mathstrut -\mathstrut 1346q^{61} \) \(\mathstrut +\mathstrut 72q^{63} \) \(\mathstrut +\mathstrut 1408q^{64} \) \(\mathstrut +\mathstrut 180q^{65} \) \(\mathstrut +\mathstrut 1200q^{66} \) \(\mathstrut +\mathstrut 332q^{67} \) \(\mathstrut +\mathstrut 1560q^{69} \) \(\mathstrut +\mathstrut 480q^{70} \) \(\mathstrut -\mathstrut 360q^{71} \) \(\mathstrut -\mathstrut 960q^{72} \) \(\mathstrut +\mathstrut 1666q^{73} \) \(\mathstrut +\mathstrut 597q^{75} \) \(\mathstrut +\mathstrut 2160q^{76} \) \(\mathstrut +\mathstrut 288q^{77} \) \(\mathstrut +\mathstrut 240q^{78} \) \(\mathstrut +\mathstrut 512q^{79} \) \(\mathstrut -\mathstrut 2763q^{81} \) \(\mathstrut -\mathstrut 1120q^{82} \) \(\mathstrut -\mathstrut 1188q^{83} \) \(\mathstrut -\mathstrut 240q^{84} \) \(\mathstrut -\mathstrut 1604q^{85} \) \(\mathstrut -\mathstrut 702q^{87} \) \(\mathstrut -\mathstrut 2880q^{88} \) \(\mathstrut -\mathstrut 630q^{89} \) \(\mathstrut -\mathstrut 240q^{90} \) \(\mathstrut -\mathstrut 80q^{91} \) \(\mathstrut +\mathstrut 3432q^{93} \) \(\mathstrut -\mathstrut 1344q^{94} \) \(\mathstrut +\mathstrut 1800q^{95} \) \(\mathstrut +\mathstrut 384q^{96} \) \(\mathstrut +\mathstrut 2026q^{97} \) \(\mathstrut +\mathstrut 324q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.4.a \(\chi_{12}(1, \cdot)\) 12.4.a.a 1 1
12.4.b \(\chi_{12}(11, \cdot)\) 12.4.b.a 4 1

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

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