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Properties

Label 252.12.bi
Level $252$
Weight $12$
Character orbit 252.bi
Rep. character $\chi_{252}(139,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1048$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.bi (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(252, [\chi])\).

Total New Old
Modular forms 1064 1064 0
Cusp forms 1048 1048 0
Eisenstein series 16 16 0

Trace form

\( 1048 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 1048 q - 2 q^{2} - 2 q^{4} - 8 q^{8} - 8 q^{9} + 506958 q^{14} - 2 q^{16} + 18646022 q^{18} - 12211754 q^{21} - 8194 q^{22} + 4960937496 q^{25} - 8388612 q^{28} + 192980484 q^{29} + 32331752 q^{30} - 1193590832 q^{32} - 1456298126 q^{36} - 16 q^{37} + 2184313876 q^{42} - 6025356548 q^{44} - 8200 q^{46} - 2 q^{49} + 2227565420 q^{50} - 16 q^{53} - 12247946532 q^{56} - 532202568 q^{57} + 8190 q^{58} + 36685050152 q^{60} - 8 q^{64} - 5345444932 q^{65} - 2074980946 q^{70} - 26158151380 q^{72} - 131012956280 q^{74} + 9766447130 q^{77} - 128611780128 q^{78} - 18208190864 q^{81} + 299690114222 q^{84} + 195312496 q^{85} - 84171056780 q^{86} + 17179869182 q^{88} - 318384303514 q^{92} + 124833223668 q^{93} - 82303524884 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

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