Properties

Label 1344.4.b
Level $1344$
Weight $4$
Character orbit 1344.b
Rep. character $\chi_{1344}(895,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $10$
Sturm bound $1024$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1344.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(1024\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

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

\( 96q + 864q^{9} + O(q^{10}) \) \( 96q + 864q^{9} - 120q^{21} - 2400q^{25} - 400q^{29} - 1024q^{37} - 752q^{53} + 3504q^{77} + 7776q^{81} - 4704q^{85} + 3696q^{93} + O(q^{100}) \)

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.b.a \(2\) \(79.299\) \(\Q(\sqrt{-3}) \) None \(0\) \(-6\) \(0\) \(-28\) \(q-3q^{3}-8\zeta_{6}q^{5}+(-14-7\zeta_{6})q^{7}+\cdots\)
1344.4.b.b \(2\) \(79.299\) \(\Q(\sqrt{-6}) \) None \(0\) \(-6\) \(0\) \(34\) \(q-3q^{3}+\beta q^{5}+(17-3\beta )q^{7}+9q^{9}+\cdots\)
1344.4.b.c \(2\) \(79.299\) \(\Q(\sqrt{-6}) \) None \(0\) \(6\) \(0\) \(-34\) \(q+3q^{3}+\beta q^{5}+(-17+3\beta )q^{7}+9q^{9}+\cdots\)
1344.4.b.d \(2\) \(79.299\) \(\Q(\sqrt{-3}) \) None \(0\) \(6\) \(0\) \(28\) \(q+3q^{3}-8\zeta_{6}q^{5}+(14+7\zeta_{6})q^{7}+9q^{9}+\cdots\)
1344.4.b.e \(8\) \(79.299\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(-24\) \(0\) \(4\) \(q-3q^{3}+\beta _{5}q^{5}-\beta _{3}q^{7}+9q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1344.4.b.f \(8\) \(79.299\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(24\) \(0\) \(-4\) \(q+3q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+9q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
1344.4.b.g \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-36\) \(0\) \(-10\) \(q-3q^{3}-\beta _{7}q^{5}+(-1-\beta _{2})q^{7}+9q^{9}+\cdots\)
1344.4.b.h \(12\) \(79.299\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(36\) \(0\) \(10\) \(q+3q^{3}-\beta _{7}q^{5}+(1+\beta _{2})q^{7}+9q^{9}+\cdots\)
1344.4.b.i \(24\) \(79.299\) None \(0\) \(-72\) \(0\) \(20\)
1344.4.b.j \(24\) \(79.299\) None \(0\) \(72\) \(0\) \(-20\)

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

\( S_{4}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)