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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1323.2.s.a \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) None \(3\) \(0\) \(-6\) \(0\) \(q+(1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-3q^{5}+(1-2\zeta_{6})q^{8}+\cdots\)
1323.2.s.b \(10\) \(10.564\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{7}-\beta _{8})q^{2}+\cdots\)
1323.2.s.c \(12\) \(10.564\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{3}+\beta _{5})q^{2}+(-\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.s.d \(48\) \(10.564\) None \(0\) \(0\) \(0\) \(0\)

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

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