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Properties

Label 252.12.x
Level $252$
Weight $12$
Character orbit 252.x
Rep. character $\chi_{252}(41,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $176$
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.x (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
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 1068 176 892
Cusp forms 1044 176 868
Eisenstein series 24 0 24

Trace form

\( 176 q - 8513 q^{7} - 9600 q^{9} + O(q^{10}) \) \( 176 q - 8513 q^{7} - 9600 q^{9} - 471234 q^{11} - 5659308 q^{15} + 11370339 q^{21} + 154612950 q^{23} - 859375000 q^{25} + 289470732 q^{29} - 642873268 q^{37} + 1540721106 q^{39} - 441618412 q^{43} - 2423533723 q^{49} - 10870145178 q^{51} + 16872743658 q^{57} + 7771317261 q^{63} - 31684138296 q^{65} + 19117152502 q^{67} + 2703353577 q^{77} - 60420441692 q^{79} - 63262726380 q^{81} + 27456431250 q^{85} + 92581843878 q^{91} - 231877269384 q^{93} + 163478833860 q^{95} - 281562072174 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{12}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)