Properties

Label 56.5.c
Level $56$
Weight $5$
Character orbit 56.c
Rep. character $\chi_{56}(41,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $40$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 56 = 2^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 56.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(40\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(56, [\chi])\).

Total New Old
Modular forms 36 8 28
Cusp forms 28 8 20
Eisenstein series 8 0 8

Trace form

\( 8 q + 56 q^{7} - 248 q^{9} - 144 q^{11} + 64 q^{15} - 320 q^{21} + 1200 q^{23} + 648 q^{25} - 1392 q^{29} - 384 q^{35} - 496 q^{37} - 704 q^{39} + 5872 q^{43} + 5896 q^{49} - 4992 q^{51} + 1680 q^{53} - 9472 q^{57}+ \cdots + 75376 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(56, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
56.5.c.a 56.c 7.b $8$ $5.789$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None 56.5.c.a \(0\) \(0\) \(0\) \(56\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(7-\beta _{5})q^{7}+(-31+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(56, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(56, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 2}\)