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Properties

Label 252.8.b
Level $252$
Weight $8$
Character orbit 252.b
Rep. character $\chi_{252}(55,\cdot)$
Character field $\Q$
Dimension $138$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 344 142 202
Cusp forms 328 138 190
Eisenstein series 16 4 12

Trace form

\( 138 q + 9 q^{2} + 89 q^{4} - 1287 q^{8} + O(q^{10}) \) \( 138 q + 9 q^{2} + 89 q^{4} - 1287 q^{8} - 16763 q^{14} + 34453 q^{16} - 68502 q^{22} - 2010766 q^{25} - 230135 q^{28} + 76340 q^{29} + 412289 q^{32} + 1049596 q^{37} + 1887990 q^{44} - 1222858 q^{46} - 778790 q^{49} + 1830309 q^{50} + 1592916 q^{53} - 269947 q^{56} + 5428450 q^{58} - 5234935 q^{64} + 1711952 q^{65} - 3636368 q^{70} + 14636398 q^{74} - 9469164 q^{77} - 6723760 q^{85} - 18560626 q^{86} + 26845802 q^{88} - 18484830 q^{92} - 31324351 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

The newforms in this space have not yet been added to the LMFDB.

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

\( S_{8}^{\mathrm{old}}(252, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)