Properties

Label 256.2.b
Level $256$
Weight $2$
Character orbit 256.b
Rep. character $\chi_{256}(129,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $3$
Sturm bound $64$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 256.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(64\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

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

Total New Old
Modular forms 44 10 34
Cusp forms 20 6 14
Eisenstein series 24 4 20

Trace form

\( 6 q + 2 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{9} - 4 q^{17} + 6 q^{25} - 16 q^{33} + 4 q^{41} + 22 q^{49} - 16 q^{57} - 8 q^{65} - 44 q^{73} - 26 q^{81} - 12 q^{89} + 28 q^{97} + O(q^{100}) \)

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.b.a 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{5}-4q^{7}-q^{9}+iq^{11}+\cdots\)
256.2.b.b 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+3q^{9}+3iq^{13}+2q^{17}+q^{25}+\cdots\)
256.2.b.c 256.b 8.b $2$ $2.044$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+iq^{11}+\cdots\)

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

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