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Properties

Label 504.2.ch
Level $504$
Weight $2$
Character orbit 504.ch
Rep. character $\chi_{504}(269,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $2$
Sturm bound $192$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 168 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 208 64 144
Cusp forms 176 64 112
Eisenstein series 32 0 32

Trace form

\( 64 q + O(q^{10}) \) \( 64 q + 4 q^{16} - 16 q^{22} + 32 q^{25} + 44 q^{28} + 60 q^{40} - 16 q^{46} + 16 q^{49} + 36 q^{52} - 44 q^{58} - 24 q^{64} - 60 q^{70} + 48 q^{73} + 16 q^{79} - 132 q^{82} + 4 q^{88} - 108 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.2.ch.a 504.ch 168.aa $8$ $4.024$ 8.0.4857532416.2 None 504.2.ch.a \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(2-2\beta _{3})q^{4}-\beta _{5}q^{5}+(3+\cdots)q^{7}+\cdots\)
504.2.ch.b 504.ch 168.aa $56$ $4.024$ None 504.2.ch.b \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(504, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(504, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)