Properties

Label 252.4.be
Level $252$
Weight $4$
Character orbit 252.be
Rep. character $\chi_{252}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 84 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 304 96 208
Cusp forms 272 96 176
Eisenstein series 32 0 32

Trace form

\( 96q + O(q^{10}) \) \( 96q - 144q^{13} - 60q^{16} + 480q^{22} + 1032q^{25} + 900q^{28} - 1008q^{34} + 504q^{37} + 492q^{40} + 120q^{46} + 1488q^{49} - 708q^{52} + 1932q^{58} - 2160q^{61} - 2376q^{64} - 588q^{70} + 1320q^{73} - 1368q^{76} - 996q^{82} + 2592q^{85} - 1524q^{88} - 3852q^{94} - 2064q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.4.be.a \(96\) \(14.868\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)