Properties

Label 12.16
Level 12
Weight 16
Dimension 31
Nonzero newspaces 2
Newforms 3
Sturm bound 128
Trace bound 1

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Defining parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newforms: \( 3 \)
Sturm bound: \(128\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(12))\).

Total New Old
Modular forms 65 35 30
Cusp forms 55 31 24
Eisenstein series 10 4 6

Trace form

\( 31q + 2187q^{3} + 26968q^{4} + 115362q^{5} + 823656q^{6} + 3709392q^{7} + 10536855q^{9} + O(q^{10}) \) \( 31q + 2187q^{3} + 26968q^{4} + 115362q^{5} + 823656q^{6} + 3709392q^{7} + 10536855q^{9} - 43831600q^{10} - 41871852q^{11} - 226414248q^{12} - 26296918q^{13} + 52396146q^{15} - 1459325408q^{16} + 3512804742q^{17} - 4234777584q^{18} + 5238674700q^{19} - 4475952456q^{21} - 2533670160q^{22} - 5842717992q^{23} - 18487781856q^{24} - 100850344911q^{25} + 10460353203q^{27} + 5481093840q^{28} + 166312147338q^{29} + 8237058960q^{30} - 81299083368q^{31} + 230643700980q^{33} + 450165745472q^{34} - 1054492684704q^{35} + 232631927160q^{36} + 64133965490q^{37} + 381280158450q^{39} + 1945471012160q^{40} - 1220472557730q^{41} + 1938106219632q^{42} + 2087694689748q^{43} - 4455341042862q^{45} + 2270790222432q^{46} - 4717686000672q^{47} + 5846474725152q^{48} - 17364113043761q^{49} + 10933578069462q^{51} - 6113229405424q^{52} - 19058082641694q^{53} + 1626598700568q^{54} + 36285020054712q^{55} + 37052040330756q^{57} - 19395437098192q^{58} - 40508760730572q^{59} - 10924219377600q^{60} + 9054167900330q^{61} + 17741906944848q^{63} + 21633892829056q^{64} - 181772821755540q^{65} + 4928819126448q^{66} + 30127015867308q^{67} + 255898488868824q^{69} + 91772543171040q^{70} - 271446469781400q^{71} + 66924493142592q^{72} + 326950045910150q^{73} + 224850754822077q^{75} - 205265768291280q^{76} - 393734977656768q^{77} + 58364283489648q^{78} + 218426580962376q^{79} + 184757194000719q^{81} - 750029796726880q^{82} - 97290581971572q^{83} - 92605433207856q^{84} - 75154133665724q^{85} + 280522924065882q^{87} - 619691835246912q^{88} - 216695712849570q^{89} - 471443548913520q^{90} + 1389408878028000q^{91} - 935248037922336q^{93} + 1301107064491200q^{94} + 854707412449800q^{95} + 525428335287168q^{96} - 2161429761173314q^{97} - 200271770088588q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(12))\)

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
12.16.a \(\chi_{12}(1, \cdot)\) 12.16.a.a 1 1
12.16.a.b 2
12.16.b \(\chi_{12}(11, \cdot)\) 12.16.b.a 28 1

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(12))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(12)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)