Properties

Label 1344.4.c
Level $1344$
Weight $4$
Character orbit 1344.c
Rep. character $\chi_{1344}(673,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $8$
Sturm bound $1024$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1024\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(5\), \(23\)

Dimensions

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

Total New Old
Modular forms 792 72 720
Cusp forms 744 72 672
Eisenstein series 48 0 48

Trace form

\( 72q - 648q^{9} + O(q^{10}) \) \( 72q - 648q^{9} + 624q^{17} - 1272q^{25} + 2832q^{41} + 3528q^{49} - 9216q^{65} + 1776q^{73} + 5832q^{81} - 528q^{89} - 10896q^{97} + O(q^{100}) \)

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.c.a \(6\) \(79.299\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(-42\) \(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.b \(6\) \(79.299\) 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(-42\) \(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.c \(6\) \(79.299\) 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(42\) \(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.d \(6\) \(79.299\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(0\) \(0\) \(42\) \(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.e \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(-84\) \(q+3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.f \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-84\) \(q-3\beta _{2}q^{3}+(\beta _{2}+\beta _{11})q^{5}-7q^{7}-9q^{9}+\cdots\)
1344.4.c.g \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(84\) \(q+3\beta _{2}q^{3}+(\beta _{2}+\beta _{11})q^{5}+7q^{7}-9q^{9}+\cdots\)
1344.4.c.h \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(84\) \(q-3\beta _{1}q^{3}+(\beta _{1}-\beta _{3})q^{5}+7q^{7}-9q^{9}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)