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Properties

Label 1323.2.s
Level $1323$
Weight $2$
Character orbit 1323.s
Rep. character $\chi_{1323}(656,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $4$
Sturm bound $336$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(336\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 384 88 296
Cusp forms 288 72 216
Eisenstein series 96 16 80

Trace form

\( 72 q - 3 q^{2} + 31 q^{4} - 6 q^{5} + O(q^{10}) \) \( 72 q - 3 q^{2} + 31 q^{4} - 6 q^{5} + 6 q^{10} - 3 q^{13} - 23 q^{16} - 9 q^{17} + 6 q^{19} - 6 q^{20} - 8 q^{22} + 42 q^{25} + 6 q^{26} - 6 q^{29} + 15 q^{31} + 69 q^{32} + 6 q^{34} + q^{37} + 54 q^{38} - 6 q^{41} - 8 q^{43} - 69 q^{44} + 16 q^{46} + 15 q^{47} - 3 q^{50} - 36 q^{53} - 2 q^{58} - 18 q^{59} - 36 q^{61} + 24 q^{62} - 28 q^{64} + 36 q^{65} + 6 q^{67} - 48 q^{68} + 6 q^{73} - 18 q^{79} - 45 q^{80} - 30 q^{83} - 21 q^{85} - 46 q^{88} + 27 q^{89} + 84 q^{92} + 3 q^{94} + 141 q^{95} - 3 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1323, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1323.2.s.a 1323.s 63.s $2$ $10.564$ \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-3q^{5}+(1-2\zeta_{6})q^{8}+\cdots\)
1323.2.s.b 1323.s 63.s $10$ $10.564$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
1323.2.s.c 1323.s 63.s $12$ $10.564$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.s.d 1323.s 63.s $48$ $10.564$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1323, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)