Properties

Label 1344.2.q
Level $1344$
Weight $2$
Character orbit 1344.q
Rep. character $\chi_{1344}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $26$
Sturm bound $512$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 26 \)
Sturm bound: \(512\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

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

\( 64q - 32q^{9} + O(q^{10}) \) \( 64q - 32q^{9} - 16q^{13} + 16q^{21} - 32q^{25} - 32q^{29} + 24q^{37} + 16q^{53} - 16q^{61} - 48q^{77} - 32q^{81} - 96q^{85} + 8q^{93} + 32q^{97} + O(q^{100}) \)

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.q.a \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(-5\) \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.b \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(1\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.c \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(5\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.d \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.e \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-5\) \(q+(-1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.f \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.g \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(1\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.h \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.q.i \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(5\) \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.j \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(-5\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.q.k \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(-1\) \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.l \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-4\) \(5\) \(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.m \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(-5\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.n \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(-1\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.o \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(1\) \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.p \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.q \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(5\) \(q+(1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.r \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-5\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.q.s \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-1\) \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.t \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(-5\) \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.u \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(1\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.v \(2\) \(10.732\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(5\) \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.q.w \(4\) \(10.732\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-2\) \(-1\) \(-6\) \(q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
1344.2.q.x \(4\) \(10.732\) \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(2\) \(-1\) \(6\) \(q+(1-\beta _{2})q^{3}+(-1+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
1344.2.q.y \(6\) \(10.732\) 6.0.1156923.1 None \(0\) \(-3\) \(0\) \(3\) \(q+(-1-\beta _{2})q^{3}+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1344.2.q.z \(6\) \(10.732\) 6.0.1156923.1 None \(0\) \(3\) \(0\) \(-3\) \(q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)