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Properties

Label 455.2.dk
Level $455$
Weight $2$
Character orbit 455.dk
Rep. character $\chi_{455}(6,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $144$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 455 = 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 455.dk (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(455, [\chi])\).

Total New Old
Modular forms 240 144 96
Cusp forms 208 144 64
Eisenstein series 32 0 32

Trace form

\( 144 q - 8 q^{7} + 64 q^{9} - 4 q^{11} + 32 q^{14} - 4 q^{15} + 48 q^{16} - 32 q^{18} - 44 q^{21} - 16 q^{22} - 88 q^{28} - 20 q^{29} - 40 q^{32} - 4 q^{35} - 48 q^{36} + 16 q^{39} + 40 q^{42} + 72 q^{43}+ \cdots + 76 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(455, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
455.2.dk.a 455.dk 91.ac $144$ $3.633$ None 455.2.dk.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(455, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(455, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)