Properties

Label 432.2.k
Level $432$
Weight $2$
Character orbit 432.k
Rep. character $\chi_{432}(109,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $4$
Sturm bound $144$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 432.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

Total New Old
Modular forms 156 64 92
Cusp forms 132 64 68
Eisenstein series 24 0 24

Trace form

\( 64q + O(q^{10}) \) \( 64q - 4q^{10} + 36q^{16} + 8q^{19} + 4q^{22} + 12q^{28} + 20q^{34} + 4q^{40} + 16q^{43} - 48q^{46} - 64q^{49} - 20q^{52} - 48q^{58} - 16q^{61} - 24q^{64} + 64q^{67} - 120q^{70} - 48q^{76} - 16q^{79} + 16q^{85} - 116q^{88} - 24q^{91} - 12q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
432.2.k.a \(4\) \(3.450\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.b \(4\) \(3.450\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.c \(24\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)
432.2.k.d \(32\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)