Properties

Label 1152.2.w
Level $1152$
Weight $2$
Character orbit 1152.w
Rep. character $\chi_{1152}(143,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $64$
Newform subspaces $2$
Sturm bound $384$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 96 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1152, [\chi])\).

Total New Old
Modular forms 832 64 768
Cusp forms 704 64 640
Eisenstein series 128 0 128

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 64 q^{55} + 64 q^{61} + 32 q^{67} + 64 q^{79} + 96 q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.2.w.a $32$ $9.199$ None \(0\) \(0\) \(0\) \(0\)
1152.2.w.b $32$ $9.199$ None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(1152, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1152, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(384, [\chi])\)\(^{\oplus 2}\)