Properties

Label 256.4.b
Level $256$
Weight $4$
Character orbit 256.b
Rep. character $\chi_{256}(129,\cdot)$
Character field $\Q$
Dimension $22$
Newform subspaces $9$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 256 = 2^{8} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 256.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(256, [\chi])\).

Total New Old
Modular forms 108 26 82
Cusp forms 84 22 62
Eisenstein series 24 4 20

Trace form

\( 22 q - 158 q^{9} - 4 q^{17} - 346 q^{25} - 112 q^{33} + 4 q^{41} - 954 q^{49} + 784 q^{57} - 1480 q^{65} - 268 q^{73} + 374 q^{81} - 172 q^{89} + 3164 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(256, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
256.4.b.a 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 8.4.a.a \(0\) \(0\) \(0\) \(-48\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}-\beta q^{5}-24 q^{7}+11 q^{9}+\cdots\)
256.4.b.b 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 128.4.a.a \(0\) \(0\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-3\beta q^{5}-20 q^{7}+23 q^{9}+\cdots\)
256.4.b.c 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 32.4.a.a \(0\) \(0\) \(0\) \(-32\) $\mathrm{SU}(2)[C_{2}]$ \(q+4\beta q^{3}+5\beta q^{5}-16 q^{7}-37 q^{9}+\cdots\)
256.4.b.d 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) 32.4.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+11\beta q^{5}+27 q^{9}+9\beta q^{13}-94 q^{17}+\cdots\)
256.4.b.e 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 32.4.a.a \(0\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{2}]$ \(q+4\beta q^{3}-5\beta q^{5}+16 q^{7}-37 q^{9}+\cdots\)
256.4.b.f 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 128.4.a.a \(0\) \(0\) \(0\) \(40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+3\beta q^{5}+20 q^{7}+23 q^{9}+\cdots\)
256.4.b.g 256.b 8.b $2$ $15.104$ \(\Q(\sqrt{-1}) \) None 8.4.a.a \(0\) \(0\) \(0\) \(48\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}+\beta q^{5}+24 q^{7}+11 q^{9}+\cdots\)
256.4.b.h 256.b 8.b $4$ $15.104$ \(\Q(\zeta_{12})\) None 128.4.a.e \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta_{2}+\beta_1)q^{3}+(2\beta_{2}+\beta_1)q^{5}+\cdots\)
256.4.b.i 256.b 8.b $4$ $15.104$ \(\Q(\zeta_{12})\) None 128.4.a.e \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta_{2}+\beta_1)q^{3}+(-2\beta_{2}-\beta_1)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(256, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(256, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(128, [\chi])\)\(^{\oplus 2}\)