Properties

Label 504.2.cc
Level $504$
Weight $2$
Character orbit 504.cc
Rep. character $\chi_{504}(293,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $184$
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.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 504 \)
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 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184 q - 6 q^{2} - 2 q^{4} - 2 q^{7} - 8 q^{9} + O(q^{10}) \) \( 184 q - 6 q^{2} - 2 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 20 q^{15} - 2 q^{16} - 18 q^{18} + 6 q^{22} - 12 q^{23} + 72 q^{25} + 4 q^{28} - 20 q^{30} + 24 q^{32} - 26 q^{36} + 4 q^{39} - 16 q^{46} - 2 q^{49} - 36 q^{50} - 24 q^{56} - 32 q^{57} + 6 q^{58} - 20 q^{60} - 30 q^{63} - 8 q^{64} - 12 q^{65} - 6 q^{70} - 12 q^{72} + 48 q^{74} - 56 q^{78} - 4 q^{79} - 24 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} + 54 q^{92} - 72 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
504.2.cc.a 504.cc 504.bc $16$ $4.024$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-14}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{11}q^{2}-\beta _{14}q^{3}+(2-2\beta _{4})q^{4}+\cdots\)
504.2.cc.b 504.cc 504.bc $168$ $4.024$ None \(-6\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$