Properties

Label 252.2.b
Level $252$
Weight $2$
Character orbit 252.b
Rep. character $\chi_{252}(55,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $5$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
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 56 22 34
Cusp forms 40 18 22
Eisenstein series 16 4 12

Trace form

\( 18 q + 3 q^{2} - 3 q^{4} + 9 q^{8} + O(q^{10}) \) \( 18 q + 3 q^{2} - 3 q^{4} + 9 q^{8} - 5 q^{14} + 5 q^{16} + 14 q^{22} - 22 q^{25} - 3 q^{28} + 20 q^{29} - 7 q^{32} - 4 q^{37} - 42 q^{44} - 22 q^{46} + 2 q^{49} - 33 q^{50} - 12 q^{53} + 29 q^{56} - 50 q^{58} - 39 q^{64} - 16 q^{65} + 48 q^{70} + 34 q^{74} - 12 q^{77} - 16 q^{85} + 74 q^{86} + 34 q^{88} + 42 q^{92} - 37 q^{98} + O(q^{100}) \)

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.b.a \(2\) \(2.012\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(0\) \(q+\beta q^{2}+(-2+\beta )q^{4}+(-1+2\beta )q^{7}+\cdots\)
252.2.b.b \(4\) \(2.012\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+\beta _{3}q^{7}-2\beta _{1}q^{8}+\cdots\)
252.2.b.c \(4\) \(2.012\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+2\beta _{2}+\cdots)q^{7}+\cdots\)
252.2.b.d \(4\) \(2.012\) 4.0.2312.1 None \(1\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
252.2.b.e \(4\) \(2.012\) 4.0.2312.1 None \(1\) \(0\) \(0\) \(2\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)

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

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