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Properties

Label 1323.2.i
Level $1323$
Weight $2$
Character orbit 1323.i
Rep. character $\chi_{1323}(521,\cdot)$
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.i (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

\( 72q - 62q^{4} - 3q^{5} + O(q^{10}) \) \( 72q - 62q^{4} - 3q^{5} + 6q^{10} - 15q^{11} + 3q^{13} + 46q^{16} + 9q^{17} + 6q^{19} + 6q^{20} - 8q^{22} - 18q^{23} - 21q^{25} - 6q^{26} - 6q^{29} - 6q^{34} + q^{37} + 27q^{38} - 24q^{40} + 6q^{41} - 8q^{43} + 69q^{44} + 16q^{46} + 30q^{47} - 3q^{50} + 15q^{52} + 36q^{53} + q^{58} - 36q^{59} - 24q^{62} - 28q^{64} - 12q^{67} - 24q^{68} + 6q^{73} - 129q^{74} + 36q^{79} + 45q^{80} + 30q^{83} - 21q^{85} + 63q^{86} + 23q^{88} - 27q^{89} + 84q^{92} + 3q^{97} + O(q^{100}) \)

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.i.a \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(0\) \(q+(-1+2\zeta_{6})q^{2}-q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
1323.2.i.b \(10\) \(10.564\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{5})q^{2}+(-1-2\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
1323.2.i.c \(12\) \(10.564\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
1323.2.i.d \(48\) \(10.564\) None \(0\) \(0\) \(0\) \(0\)

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

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