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Properties

Label 504.2.bm
Level $504$
Weight $2$
Character orbit 504.bm
Rep. character $\chi_{504}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
Sturm bound $192$
Trace bound $2$

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Defining parameters

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

\( 64 q + O(q^{10}) \) \( 64 q + 4 q^{16} - 16 q^{22} - 32 q^{25} + 20 q^{28} + 80 q^{34} - 52 q^{40} + 24 q^{46} + 16 q^{49} + 28 q^{52} + 36 q^{58} - 24 q^{64} + 16 q^{67} - 12 q^{70} - 16 q^{73} - 120 q^{76} - 28 q^{82} - 52 q^{88} - 48 q^{91} + 12 q^{94} + 32 q^{97} + O(q^{100}) \)

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.bm.a 504.bm 168.v $8$ $4.024$ \(\Q(\zeta_{24})\) None 504.2.bm.a \(-4\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{24}+\zeta_{24}^{2})q^{2}+(2\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{4}+\cdots\)
504.2.bm.b 504.bm 168.v $8$ $4.024$ \(\Q(\zeta_{24})\) None 504.2.bm.a \(4\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\zeta_{24}-\zeta_{24}^{2})q^{2}+(-2\zeta_{24}+2\zeta_{24}^{3}+\cdots)q^{4}+\cdots\)
504.2.bm.c 504.bm 168.v $48$ $4.024$ None 504.2.bm.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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