Properties

Label 1344.2.i
Level $1344$
Weight $2$
Character orbit 1344.i
Rep. character $\chi_{1344}(545,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $7$
Sturm bound $512$
Trace bound $21$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.i (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(512\)
Trace bound: \(21\)
Distinguishing \(T_p\): \(5\), \(13\), \(19\), \(29\)

Dimensions

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

Total New Old
Modular forms 280 64 216
Cusp forms 232 64 168
Eisenstein series 48 0 48

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 64 q^{25} - 16 q^{49} - 96 q^{81} + O(q^{100}) \)

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.i.a 1344.i 168.i $4$ $10.732$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{12}q^{3}+(\zeta_{12}-\zeta_{12}^{3})q^{7}+3q^{9}+\cdots\)
1344.2.i.b 1344.i 168.i $4$ $10.732$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{12}q^{3}+(-\zeta_{12}+\zeta_{12}^{3})q^{7}+3q^{9}+\cdots\)
1344.2.i.c 1344.i 168.i $8$ $10.732$ 8.0.49787136.1 \(\Q(\sqrt{-42}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{7}-3q^{9}+\beta _{7}q^{13}+\cdots\)
1344.2.i.d 1344.i 168.i $8$ $10.732$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-2\beta _{2}-\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1344.2.i.e 1344.i 168.i $8$ $10.732$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-2\beta _{2}-\beta _{7})q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1344.2.i.f 1344.i 168.i $16$ $10.732$ 16.0.\(\cdots\).1 None \(0\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{6})q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+(-1+\cdots)q^{9}+\cdots\)
1344.2.i.g 1344.i 168.i $16$ $10.732$ 16.0.\(\cdots\).1 None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{6})q^{3}+\beta _{5}q^{5}+\beta _{3}q^{7}+(-1+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)