Properties

Label 256.3.f
Level $256$
Weight $3$
Character orbit 256.f
Rep. character $\chi_{256}(63,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $4$
Sturm bound $96$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 256.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

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

Total New Old
Modular forms 152 32 120
Cusp forms 104 32 72
Eisenstein series 48 0 48

Trace form

\( 32q + O(q^{10}) \) \( 32q + 224q^{49} - 192q^{65} - 288q^{81} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
256.3.f.a \(8\) \(6.975\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-16\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(-2-2\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
256.3.f.b \(8\) \(6.975\) 8.0.8540717056.1 None \(0\) \(0\) \(-16\) \(0\) \(q+\beta _{2}q^{3}+(-2-2\beta _{1}-\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
256.3.f.c \(8\) \(6.975\) 8.0.8540717056.1 None \(0\) \(0\) \(16\) \(0\) \(q+\beta _{2}q^{3}+(2+2\beta _{1}+\beta _{6})q^{5}+(\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
256.3.f.d \(8\) \(6.975\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(16\) \(0\) \(q+\zeta_{24}^{2}q^{3}+(2+2\zeta_{24}-\zeta_{24}^{4})q^{5}+\cdots\)

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

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