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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1344.2.q.a 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.b 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.c 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.d 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.e 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-2-\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.f 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.g 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.h 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.q.i 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.j 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.q.k 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.l 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1344.2.q.m 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.n 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.o 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.p 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2-3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.q 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1344.2.q.r 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots\)
1344.2.q.s 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1344.2.q.t 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1344.2.q.u 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+3\zeta_{6})q^{7}+\cdots\)
1344.2.q.v 1344.q 7.c $2$ $10.732$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1344.2.q.w 1344.q 7.c $4$ $10.732$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(-2\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
1344.2.q.x 1344.q 7.c $4$ $10.732$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(0\) \(2\) \(-1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{3}+(-1+2\beta _{1}-\beta _{3})q^{5}+\cdots\)
1344.2.q.y 1344.q 7.c $6$ $10.732$ 6.0.1156923.1 None \(0\) \(-3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{3}+\beta _{4}q^{5}+(1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1344.2.q.z 1344.q 7.c $6$ $10.732$ 6.0.1156923.1 None \(0\) \(3\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{3}+\beta _{4}q^{5}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)

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

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