Properties

Label 6.23.b
Level $6$
Weight $23$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $23$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 23 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(23\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{23}(6, [\chi])\).

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

Trace form

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

Decomposition of \(S_{23}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.23.b.a 6.b 3.b $8$ $18.402$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-69720\) \(0\) \(5645581840\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-8715+9\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{23}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{23}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{23}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)