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Properties

Label 252.8.e
Level $252$
Weight $8$
Character orbit 252.e
Rep. character $\chi_{252}(71,\cdot)$
Character field $\Q$
Dimension $84$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(252, [\chi])\).

Total New Old
Modular forms 344 84 260
Cusp forms 328 84 244
Eisenstein series 16 0 16

Trace form

\( 84 q + 104 q^{4} + O(q^{10}) \) \( 84 q + 104 q^{4} - 5816 q^{10} + 16684 q^{16} - 201700 q^{22} - 1312500 q^{25} + 39788 q^{28} - 400048 q^{34} - 165544 q^{37} - 1477624 q^{40} + 1616724 q^{46} - 9882516 q^{49} - 3744592 q^{52} + 12053212 q^{58} - 8764504 q^{61} - 5645200 q^{64} + 8997576 q^{70} - 38069208 q^{76} + 24696392 q^{82} - 29977064 q^{85} - 48692036 q^{88} + 73638456 q^{94} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
252.8.e.a 252.e 12.b $84$ $78.721$ None 252.8.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)