Properties

Label 448.1.l
Level $448$
Weight $1$
Character orbit 448.l
Rep. character $\chi_{448}(209,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $2$
Newform subspaces $1$
Sturm bound $64$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 448.l (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(448, [\chi])\).

Total New Old
Modular forms 24 6 18
Cusp forms 8 2 6
Eisenstein series 16 4 12

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 2 0 0 0

Trace form

\( 2 q + O(q^{10}) \) \( 2 q + 2 q^{11} - 2 q^{29} - 2 q^{37} - 2 q^{43} - 2 q^{49} + 2 q^{53} - 2 q^{63} - 2 q^{67} + 2 q^{77} - 2 q^{81} + 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(448, [\chi])\) into newform subspaces

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
448.1.l.a $2$ $0.224$ \(\Q(\sqrt{-1}) \) $D_{4}$ \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}-iq^{9}+(1+i)q^{11}+iq^{25}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(448, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(448, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)