Properties

Label 324.2.b
Level $324$
Weight $2$
Character orbit 324.b
Rep. character $\chi_{324}(323,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $3$
Sturm bound $108$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(108\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(324, [\chi])\).

Total New Old
Modular forms 66 28 38
Cusp forms 42 20 22
Eisenstein series 24 8 16

Trace form

\( 20q + 2q^{4} + O(q^{10}) \) \( 20q + 2q^{4} - 8q^{10} + 4q^{13} + 14q^{16} + 6q^{22} - 24q^{28} + 10q^{34} + 4q^{37} + 4q^{40} - 24q^{46} + 8q^{49} - 32q^{52} - 20q^{58} - 8q^{61} + 2q^{64} - 24q^{70} + 4q^{73} - 54q^{76} + 46q^{82} - 28q^{85} - 18q^{88} - 12q^{94} - 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(324, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
324.2.b.a \(4\) \(2.587\) \(\Q(\sqrt{-2}, \sqrt{3})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\)
324.2.b.b \(8\) \(2.587\) 8.0.170772624.1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{3}q^{2}-\beta _{2}q^{4}+(\beta _{3}-\beta _{4}+\beta _{7})q^{5}+\cdots\)
324.2.b.c \(8\) \(2.587\) 8.0.5780865024.3 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{3}+\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(324, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(324, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 2}\)