Properties

Label 1323.2.g
Level $1323$
Weight $2$
Character orbit 1323.g
Rep. character $\chi_{1323}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $8$
Sturm bound $336$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(336\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

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

\( 72q + q^{2} - 33q^{4} - 10q^{5} + 12q^{8} + O(q^{10}) \) \( 72q + q^{2} - 33q^{4} - 10q^{5} + 12q^{8} + 6q^{10} + 6q^{11} + 3q^{13} - 27q^{16} + 9q^{17} + 4q^{20} + 8q^{23} + 42q^{25} + 16q^{26} + 18q^{29} + 3q^{31} - 41q^{32} + 3q^{37} - 38q^{38} - 12q^{40} + 10q^{41} + 11q^{44} - 12q^{46} + 27q^{47} + 45q^{50} - 30q^{52} - 16q^{53} + 6q^{55} - 18q^{58} + 30q^{59} - 12q^{62} + 12q^{64} - 30q^{65} + 6q^{67} - 60q^{68} - 6q^{71} - 12q^{73} + 82q^{74} - 6q^{76} + 18q^{79} + 19q^{80} + 18q^{83} + 3q^{85} + 50q^{86} + 18q^{88} + 41q^{89} + 52q^{92} + 3q^{94} + 17q^{95} + 3q^{97} + O(q^{100}) \)

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.g.a \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(0\) \(q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-q^{5}+3q^{8}+\cdots\)
1323.2.g.b \(6\) \(10.564\) 6.0.309123.1 None \(-1\) \(0\) \(-10\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1323.2.g.c \(6\) \(10.564\) 6.0.309123.1 None \(-1\) \(0\) \(10\) \(0\) \(q+(\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{2}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
1323.2.g.d \(6\) \(10.564\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(-6\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
1323.2.g.e \(6\) \(10.564\) \(\Q(\zeta_{18})\) None \(3\) \(0\) \(6\) \(0\) \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
1323.2.g.f \(10\) \(10.564\) 10.0.\(\cdots\).1 None \(-2\) \(0\) \(-8\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{7})q^{4}+(-1+\cdots)q^{5}+\cdots\)
1323.2.g.g \(12\) \(10.564\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}+(-\beta _{1}+\beta _{4}-\beta _{5}+\beta _{6}-\beta _{7}+\cdots)q^{4}+\cdots\)
1323.2.g.h \(24\) \(10.564\) None \(-4\) \(0\) \(0\) \(0\)

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

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