Properties

Label 252.2.e
Level $252$
Weight $2$
Character orbit 252.e
Rep. character $\chi_{252}(71,\cdot)$
Character field $\Q$
Dimension $12$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
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 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

Trace form

\( 12 q + 8 q^{4} + O(q^{10}) \) \( 12 q + 8 q^{4} - 8 q^{10} - 20 q^{16} + 20 q^{22} - 12 q^{25} - 4 q^{28} - 16 q^{34} + 8 q^{37} + 8 q^{40} - 36 q^{46} - 12 q^{49} - 16 q^{52} + 4 q^{58} + 56 q^{61} - 16 q^{64} + 24 q^{70} + 72 q^{76} + 56 q^{82} - 56 q^{85} + 28 q^{88} - 24 q^{94} + O(q^{100}) \)

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.e.a 252.e 12.b $12$ $2.012$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{7}-\beta _{9}-\beta _{10}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)