Properties

Label 1344.2.bl
Level $1344$
Weight $2$
Character orbit 1344.bl
Rep. character $\chi_{1344}(703,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $12$
Sturm bound $512$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 12 \)
Sturm bound: \(512\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

Total New Old
Modular forms 560 64 496
Cusp forms 464 64 400
Eisenstein series 96 0 96

Trace form

\( 64q - 32q^{9} + O(q^{10}) \) \( 64q - 32q^{9} - 16q^{21} + 32q^{25} + 32q^{29} - 24q^{37} + 16q^{53} + 48q^{77} - 32q^{81} - 96q^{85} + 8q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1344.2.bl.a \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-6\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bl.b \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-3\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.bl.c \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(5\) \(q+(-1+\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.bl.d \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(6\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1344.2.bl.e \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-6\) \(1\) \(q+(1-\zeta_{6})q^{3}+(-4+2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.bl.f \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(1\) \(q+(1-\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.bl.g \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(-5\) \(q+(1-\zeta_{6})q^{3}+(2-\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.bl.h \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(6\) \(1\) \(q+(1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.bl.i \(8\) \(10.732\) 8.0.562828176.1 None \(0\) \(-4\) \(0\) \(-2\) \(q+(-1+\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bl.j \(8\) \(10.732\) 8.0.562828176.1 None \(0\) \(4\) \(0\) \(2\) \(q+(1-\beta _{1})q^{3}+(-\beta _{2}-\beta _{5})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1344.2.bl.k \(16\) \(10.732\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(0\) \(4\) \(q+(-1+\beta _{1})q^{3}-\beta _{7}q^{5}+(\beta _{1}+\beta _{6}+\cdots)q^{7}+\cdots\)
1344.2.bl.l \(16\) \(10.732\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(-4\) \(q+(1-\beta _{1})q^{3}-\beta _{7}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

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