Properties

Label 324.2.h
Level $324$
Weight $2$
Character orbit 324.h
Rep. character $\chi_{324}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $44$
Newform subspaces $6$
Sturm bound $108$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 324 = 2^{2} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 324.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(108\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

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

Total New Old
Modular forms 132 52 80
Cusp forms 84 44 40
Eisenstein series 48 8 40

Trace form

\( 44 q + 2 q^{4} + O(q^{10}) \) \( 44 q + 2 q^{4} + 4 q^{10} + 4 q^{13} + 2 q^{16} + 6 q^{22} + 18 q^{25} + 12 q^{28} - 32 q^{34} - 8 q^{37} - 38 q^{40} - 72 q^{46} + 14 q^{49} - 8 q^{52} - 20 q^{58} + 4 q^{61} - 100 q^{64} - 18 q^{70} - 32 q^{73} + 24 q^{76} - 32 q^{82} - 16 q^{85} + 78 q^{88} + 84 q^{94} - 8 q^{97} + O(q^{100}) \)

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.h.a \(4\) \(2.587\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{3}q^{2}-2q^{4}+2\beta _{1}q^{5}+(2-\beta _{2}+\cdots)q^{7}+\cdots\)
324.2.h.b \(4\) \(2.587\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-6\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+2\beta _{1}q^{5}+(-2+\cdots)q^{7}+\cdots\)
324.2.h.c \(4\) \(2.587\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}-\beta _{3})q^{2}+(2-2\beta _{2})q^{4}+\beta _{1}q^{5}+\cdots\)
324.2.h.d \(8\) \(2.587\) 8.0.12960000.1 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{7})q^{2}+(-\beta _{1}-\beta _{2})q^{4}+\cdots\)
324.2.h.e \(8\) \(2.587\) \(\Q(\zeta_{24})\) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{3}q^{2}+(2-2\zeta_{24})q^{4}+(\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
324.2.h.f \(16\) \(2.587\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{15}q^{2}+(-1+\beta _{8}-\beta _{9}-\beta _{11}+\cdots)q^{4}+\cdots\)

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

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