Properties

Label 252.2.b
Level 252
Weight 2
Character orbit b
Rep. character \(\chi_{252}(55,\cdot)\)
Character field \(\Q\)
Dimension 18
Newforms 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: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(252, [\chi])\) into irreducible Hecke orbits

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

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