Properties

Label 1323.2.c
Level $1323$
Weight $2$
Character orbit 1323.c
Rep. character $\chi_{1323}(1322,\cdot)$
Character field $\Q$
Dimension $54$
Newform subspaces $6$
Sturm bound $336$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(336\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1323, [\chi])\).

Total New Old
Modular forms 192 54 138
Cusp forms 144 54 90
Eisenstein series 48 0 48

Trace form

\( 54q - 56q^{4} + O(q^{10}) \) \( 54q - 56q^{4} + 92q^{16} + 48q^{22} + 38q^{25} + 24q^{37} + 6q^{43} - 12q^{46} - 104q^{58} - 144q^{64} + 44q^{67} - 36q^{79} + 44q^{85} - 20q^{88} + O(q^{100}) \)

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.c.a \(2\) \(10.564\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{4}-4\zeta_{6}q^{13}+4q^{16}-3\zeta_{6}q^{19}+\cdots\)
1323.2.c.b \(4\) \(10.564\) \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-3q^{4}-\beta _{1}q^{8}-2\beta _{1}q^{11}+\cdots\)
1323.2.c.c \(4\) \(10.564\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{5}+2\beta _{1}q^{8}+2\beta _{2}q^{10}+\cdots\)
1323.2.c.d \(12\) \(10.564\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{8}q^{2}+(-1-\beta _{6})q^{4}+\beta _{1}q^{5}+(-\beta _{8}+\cdots)q^{8}+\cdots\)
1323.2.c.e \(16\) \(10.564\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+(-1-\beta _{1}-\beta _{4})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
1323.2.c.f \(16\) \(10.564\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{5}q^{2}+(-1+\beta _{13})q^{4}-\beta _{2}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1323, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 2}\)