Properties

Label 252.4.e
Level $252$
Weight $4$
Character orbit 252.e
Rep. character $\chi_{252}(71,\cdot)$
Character field $\Q$
Dimension $36$
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.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
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 152 36 116
Cusp forms 136 36 100
Eisenstein series 16 0 16

Trace form

\( 36q - 24q^{4} + O(q^{10}) \) \( 36q - 24q^{4} + 264q^{10} - 468q^{16} + 444q^{22} - 900q^{25} - 84q^{28} - 432q^{34} - 264q^{37} + 1416q^{40} + 180q^{46} - 1764q^{49} + 2736q^{52} + 636q^{58} - 3960q^{61} + 1392q^{64} - 504q^{70} - 2520q^{76} + 1032q^{82} - 3144q^{85} + 2748q^{88} + 5496q^{94} + O(q^{100}) \)

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.e.a \(36\) \(14.868\) None \(0\) \(0\) \(0\) \(0\)

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

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