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Properties

Label 1323.2.o
Level $1323$
Weight $2$
Character orbit 1323.o
Rep. character $\chi_{1323}(440,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $5$
Sturm bound $336$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.o (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(336\)
Trace bound: \(13\)
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

\( 72q - 6q^{2} + 34q^{4} + O(q^{10}) \) \( 72q - 6q^{2} + 34q^{4} + 6q^{11} - 26q^{16} + 4q^{22} + 36q^{23} - 18q^{25} + 48q^{29} - 42q^{32} + 4q^{37} + 4q^{43} + 16q^{46} - 30q^{50} - 2q^{58} - 40q^{64} - 108q^{65} - 12q^{67} + 66q^{74} - 6q^{85} + 90q^{86} - 22q^{88} + 84q^{92} - 42q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.o.a \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(-3\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-3\zeta_{6}q^{5}+\cdots\)
1323.2.o.b \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(3\) \(0\) \(q+(-1-\zeta_{6})q^{2}+\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1323.2.o.c \(10\) \(10.564\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.o.d \(10\) \(10.564\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(1+\beta _{2}+\beta _{5}+\cdots)q^{4}+\cdots\)
1323.2.o.e \(48\) \(10.564\) None \(0\) \(0\) \(0\) \(0\)

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

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