Properties

Label 256.3.h
Level $256$
Weight $3$
Character orbit 256.h
Rep. character $\chi_{256}(31,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $56$
Newform subspaces $2$
Sturm bound $96$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 256.h (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(256, [\chi])\).

Total New Old
Modular forms 288 72 216
Cusp forms 224 56 168
Eisenstein series 64 16 48

Trace form

\( 56 q + 8 q^{5} - 8 q^{9} + O(q^{10}) \) \( 56 q + 8 q^{5} - 8 q^{9} + 8 q^{13} + 8 q^{21} - 8 q^{25} + 8 q^{29} - 16 q^{33} + 8 q^{37} - 8 q^{41} + 80 q^{45} + 328 q^{53} - 8 q^{57} + 136 q^{61} - 16 q^{65} - 376 q^{69} - 8 q^{73} - 440 q^{77} - 192 q^{85} - 8 q^{89} - 64 q^{93} - 16 q^{97} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.3.h.a 256.h 32.h $28$ $6.975$ None \(0\) \(-4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{8}]$
256.3.h.b 256.h 32.h $28$ $6.975$ None \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{3}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(256, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)