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Properties

Label 252.2.bm
Level $252$
Weight $2$
Character orbit 252.bm
Rep. character $\chi_{252}(173,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bm (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 108 16 92
Cusp forms 84 16 68
Eisenstein series 24 0 24

Trace form

\( 16 q - q^{7} + O(q^{10}) \) \( 16 q - q^{7} + 3 q^{13} - 3 q^{15} - 9 q^{17} + 16 q^{25} - 9 q^{27} + 6 q^{29} + 6 q^{31} - 27 q^{33} + 15 q^{35} + q^{37} - 3 q^{39} + 6 q^{41} - 2 q^{43} - 15 q^{45} - 18 q^{47} + 13 q^{49} + 15 q^{51} + 15 q^{57} - 15 q^{59} + 3 q^{61} - 9 q^{63} - 39 q^{65} - 7 q^{67} - 21 q^{69} - 15 q^{75} - 45 q^{77} - q^{79} + 6 q^{85} - 3 q^{87} - 21 q^{89} + 9 q^{91} - 69 q^{93} + 6 q^{95} + 3 q^{97} - 9 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.2.bm.a 252.bm 63.s $16$ $2.012$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}-\beta _{10})q^{3}+(\beta _{7}-\beta _{11})q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)