Properties

Label 1344.4.p
Level $1344$
Weight $4$
Character orbit 1344.p
Rep. character $\chi_{1344}(223,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $4$
Sturm bound $1024$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(1024\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1344, [\chi])\).

Total New Old
Modular forms 792 96 696
Cusp forms 744 96 648
Eisenstein series 48 0 48

Trace form

\( 96q - 864q^{9} + O(q^{10}) \) \( 96q - 864q^{9} + 2400q^{25} - 720q^{49} - 672q^{57} + 7776q^{81} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.4.p.a \(16\) \(79.299\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta _{1}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
1344.4.p.b \(16\) \(79.299\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-3\beta _{1}q^{3}+\beta _{7}q^{5}+(\beta _{1}-\beta _{5})q^{7}-9q^{9}+\cdots\)
1344.4.p.c \(32\) \(79.299\) None \(0\) \(0\) \(0\) \(0\)
1344.4.p.d \(32\) \(79.299\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)