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Properties

Label 6.23
Level 6
Weight 23
Dimension 8
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 46
Trace bound 0

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Defining parameters

Level: \( N \) = \( 6 = 2 \cdot 3 \)
Weight: \( k \) = \( 23 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(46\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(\Gamma_1(6))\).

Total New Old
Modular forms 24 8 16
Cusp forms 20 8 12
Eisenstein series 4 0 4

Trace form

\( 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9} + O(q^{10}) \) \( 8 q - 69720 q^{3} - 16777216 q^{4} + 156352512 q^{6} + 5645581840 q^{7} - 53592329016 q^{9} + 46180761600 q^{10} + 146213437440 q^{12} - 2875682381360 q^{13} - 731868641280 q^{15} + 35184372088832 q^{16} - 55595702845440 q^{18} - 314803957551536 q^{19} + 661593766080336 q^{21} - 511896111513600 q^{22} - 327894983245824 q^{24} - 6264418212884920 q^{25} + 11756777174853480 q^{27} - 11839643246919680 q^{28} + 51661456814407680 q^{30} - 110293228249214576 q^{31} + 256091518967454720 q^{33} - 100789882794934272 q^{34} + 112391259980562432 q^{36} - 752490366563284400 q^{37} + 1437242122292286480 q^{39} - 96848076550963200 q^{40} + 255515905807319040 q^{42} - 1301015563442074160 q^{43} - 4916408514089748480 q^{45} + 1601638996847296512 q^{46} - 306631802754170880 q^{48} + 12029391373660580760 q^{49} - 18532151948158119936 q^{51} + 6030743057433886720 q^{52} - 18559682184349532160 q^{54} + 56456085576783974400 q^{55} - 35832783024333133680 q^{57} + 34659140078143242240 q^{58} + 1534839784797634560 q^{60} - 124415281411828286768 q^{61} + 223305694023597186960 q^{63} - 73786976294838206464 q^{64} + 122984956040514011136 q^{66} - 349673137262790165680 q^{67} + 217762533639160621056 q^{69} - 485339414077397729280 q^{70} + 116592639413720186880 q^{72} - 65576379188480063600 q^{73} + 923803988759061007080 q^{75} + 660191749187118825472 q^{76} - 1049693699266563440640 q^{78} - 325232563432330354544 q^{79} - 2780170203320395644024 q^{81} + 2935193462963889438720 q^{82} - 1387462689722908803072 q^{84} + 6970706743345629511680 q^{85} - 3070393070764643665920 q^{87} + 1073523954052969267200 q^{88} - 4943089610251404410880 q^{90} - 6363735561736496595040 q^{91} + 3617627578345665462480 q^{93} + 2855373122028803850240 q^{94} + 687645619903946293248 q^{96} - 23922503524683181095920 q^{97} + 36535312526138292658176 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{23}^{\mathrm{new}}(\Gamma_1(6))\)

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
6.23.b \(\chi_{6}(5, \cdot)\) 6.23.b.a 8 1

Decomposition of \(S_{23}^{\mathrm{old}}(\Gamma_1(6))\) into lower level spaces

\( S_{23}^{\mathrm{old}}(\Gamma_1(6)) \cong \) \(S_{23}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)