Properties

Label 252.2.bf
Level $252$
Weight $2$
Character orbit 252.bf
Rep. character $\chi_{252}(19,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $36$
Newform subspaces $7$
Sturm bound $96$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 7 \)
Sturm bound: \(96\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(252, [\chi])\).

Total New Old
Modular forms 112 44 68
Cusp forms 80 36 44
Eisenstein series 32 8 24

Trace form

\( 36q + 6q^{5} + O(q^{10}) \) \( 36q + 6q^{5} + 6q^{10} + 20q^{14} + 4q^{16} + 6q^{17} - 20q^{22} + 4q^{25} - 18q^{26} + 24q^{28} + 16q^{29} - 20q^{32} - 14q^{37} - 36q^{38} - 48q^{40} - 26q^{46} - 20q^{49} - 12q^{50} - 36q^{52} + 6q^{53} - 56q^{56} - 4q^{58} - 18q^{61} - 24q^{64} - 20q^{65} + 36q^{68} - 30q^{70} - 42q^{73} + 44q^{74} - 6q^{77} + 96q^{80} + 24q^{82} - 20q^{85} + 10q^{86} + 56q^{88} - 54q^{89} + 48q^{92} + 78q^{94} + 94q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.2.bf.a \(4\) \(2.012\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(-1\) \(0\) \(6\) \(0\) \(q-\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(2-\beta _{2}+\cdots)q^{5}+\cdots\)
252.2.bf.b \(4\) \(2.012\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{3}q^{2}-2q^{4}-2\beta _{1}q^{5}+(1-3\beta _{2}+\cdots)q^{7}+\cdots\)
252.2.bf.c \(4\) \(2.012\) \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{2}+2\beta _{2}q^{4}+(2\beta _{1}-2\beta _{3})q^{5}+\cdots\)
252.2.bf.d \(4\) \(2.012\) \(\Q(\sqrt{-3}, \sqrt{-7})\) None \(1\) \(0\) \(-6\) \(0\) \(q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-2+\beta _{2}+\cdots)q^{5}+\cdots\)
252.2.bf.e \(4\) \(2.012\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(6\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+2\zeta_{12}q^{4}+\cdots\)
252.2.bf.f \(8\) \(2.012\) 8.0.562828176.1 None \(-1\) \(0\) \(0\) \(-2\) \(q+\beta _{5}q^{2}+(-\beta _{4}+\beta _{6}-\beta _{7})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
252.2.bf.g \(8\) \(2.012\) 8.0.562828176.1 None \(-1\) \(0\) \(0\) \(2\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{2}-\beta _{6}+\beta _{7})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

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