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Properties

Label 819.2.ct
Level $819$
Weight $2$
Character orbit 819.ct
Rep. character $\chi_{819}(127,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $68$
Newform subspaces $4$
Sturm bound $224$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.ct (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(224\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(819, [\chi])\).

Total New Old
Modular forms 240 68 172
Cusp forms 208 68 140
Eisenstein series 32 0 32

Trace form

\( 68 q + 32 q^{4} + O(q^{10}) \) \( 68 q + 32 q^{4} - 8 q^{10} + 6 q^{11} - 8 q^{13} + 8 q^{14} - 20 q^{16} - 4 q^{17} - 12 q^{20} + 22 q^{22} + 20 q^{23} - 68 q^{25} + 2 q^{26} - 8 q^{29} - 36 q^{32} - 10 q^{35} - 6 q^{37} + 52 q^{38} - 28 q^{40} - 18 q^{41} - 14 q^{43} - 12 q^{46} + 34 q^{49} - 42 q^{50} + 58 q^{52} + 4 q^{53} - 6 q^{55} + 12 q^{56} - 24 q^{58} + 66 q^{59} + 2 q^{61} + 8 q^{62} - 92 q^{64} + 4 q^{65} + 48 q^{67} - 8 q^{68} + 24 q^{71} - 30 q^{74} - 42 q^{76} - 24 q^{77} - 56 q^{79} - 72 q^{80} - 54 q^{82} - 12 q^{85} + 18 q^{88} - 84 q^{89} - 2 q^{91} + 112 q^{92} + 52 q^{94} + 50 q^{95} + 30 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(819, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
819.2.ct.a 819.ct 13.e $12$ $6.540$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{4}+\beta _{6}-\beta _{10})q^{2}+(1+\beta _{1}+\cdots)q^{4}+\cdots\)
819.2.ct.b 819.ct 13.e $16$ $6.540$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(1+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{15})q^{4}+\cdots\)
819.2.ct.c 819.ct 13.e $16$ $6.540$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{14}q^{2}+(2+2\beta _{5}+\beta _{7}+\beta _{13})q^{4}+\cdots\)
819.2.ct.d 819.ct 13.e $24$ $6.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(819, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(819, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)