Properties

Label 256.2.e
Level $256$
Weight $2$
Character orbit 256.e
Rep. character $\chi_{256}(65,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $16$
Newform subspaces $2$
Sturm bound $64$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(64\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(256, [\chi])\).

Total New Old
Modular forms 88 16 72
Cusp forms 40 16 24
Eisenstein series 48 0 48

Trace form

\( 16 q + O(q^{10}) \) \( 16 q - 16 q^{49} - 96 q^{65} - 16 q^{81} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.2.e.a 256.e 16.e $8$ $2.044$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}-\zeta_{24}^{7}q^{5}+(\zeta_{24}^{2}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
256.2.e.b 256.e 16.e $8$ $2.044$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{24}^{2}q^{3}+\zeta_{24}^{7}q^{5}+(-\zeta_{24}^{2}+\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)