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Properties

Label 1323.2.h
Level $1323$
Weight $2$
Character orbit 1323.h
Rep. character $\chi_{1323}(226,\cdot)$
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.h (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

\( 72q - 2q^{2} + 66q^{4} + 5q^{5} + 12q^{8} + O(q^{10}) \) \( 72q - 2q^{2} + 66q^{4} + 5q^{5} + 12q^{8} + 6q^{10} - 3q^{11} + 3q^{13} + 54q^{16} + 9q^{17} + 4q^{20} - 4q^{23} - 21q^{25} + 16q^{26} + 18q^{29} - 6q^{31} + 82q^{32} + 3q^{37} + 19q^{38} + 6q^{40} + 10q^{41} + 11q^{44} - 12q^{46} - 54q^{47} + 45q^{50} + 15q^{52} - 16q^{53} + 6q^{55} + 9q^{58} - 60q^{59} - 12q^{62} + 12q^{64} + 60q^{65} - 12q^{67} + 30q^{68} - 6q^{71} - 12q^{73} - 41q^{74} - 6q^{76} - 36q^{79} + 19q^{80} + 18q^{83} + 3q^{85} - 25q^{86} - 9q^{88} + 41q^{89} + 52q^{92} - 6q^{94} - 34q^{95} + 3q^{97} + O(q^{100}) \)

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

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

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