Properties

Label 1344.2.u
Level $1344$
Weight $2$
Character orbit 1344.u
Rep. character $\chi_{1344}(559,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $1$
Sturm bound $512$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(512\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 544 64 480
Cusp forms 480 64 416
Eisenstein series 64 0 64

Trace form

\( 64 q + O(q^{10}) \) \( 64 q - 8 q^{11} + 16 q^{23} + 16 q^{29} - 24 q^{35} + 16 q^{37} + 8 q^{43} + 16 q^{53} - 56 q^{67} + 128 q^{71} - 64 q^{81} - 8 q^{91} + 8 q^{99} + O(q^{100}) \)

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.u.a 1344.u 112.j $64$ $10.732$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(448, [\chi])\)\(^{\oplus 2}\)