Properties

Label 252.4.b
Level $252$
Weight $4$
Character orbit 252.b
Rep. character $\chi_{252}(55,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $7$
Sturm bound $192$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(192\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

Total New Old
Modular forms 152 62 90
Cusp forms 136 58 78
Eisenstein series 16 4 12

Trace form

\( 58q + q^{2} - 7q^{4} - 23q^{8} + O(q^{10}) \) \( 58q + q^{2} - 7q^{4} - 23q^{8} - 67q^{14} - 43q^{16} - 182q^{22} - 1086q^{25} - 199q^{28} - 140q^{29} - 559q^{32} - 516q^{37} + 454q^{44} - 250q^{46} - 694q^{49} + 1229q^{50} + 20q^{53} + 133q^{56} + 66q^{58} + 2153q^{64} - 1008q^{65} - 848q^{70} - 498q^{74} - 1324q^{77} + 2320q^{85} - 1138q^{86} + 346q^{88} - 1918q^{92} + 1625q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.4.b.a \(2\) \(14.868\) \(\Q(\sqrt{-7}) \) \(\Q(\sqrt{-7}) \) \(-5\) \(0\) \(0\) \(0\) \(q+(-3+\beta )q^{2}+(7-5\beta )q^{4}+(-7+14\beta )q^{7}+\cdots\)
252.4.b.b \(4\) \(14.868\) \(\Q(\sqrt{-2}, \sqrt{7})\) \(\Q(\sqrt{-21}) \) \(0\) \(0\) \(0\) \(0\) \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}-7\beta _{3}q^{7}+\cdots\)
252.4.b.c \(4\) \(14.868\) \(\Q(i, \sqrt{7})\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{2}+(-2-5\beta _{2})q^{4}+(-7+14\beta _{2}+\cdots)q^{7}+\cdots\)
252.4.b.d \(8\) \(14.868\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(0\) \(0\) \(0\) \(q+(1-\beta _{2})q^{2}+(-2-\beta _{2}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
252.4.b.e \(12\) \(14.868\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(0\) \(-10\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{8})q^{5}+\cdots\)
252.4.b.f \(12\) \(14.868\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(0\) \(0\) \(10\) \(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(\beta _{2}-\beta _{8})q^{5}+(1+\cdots)q^{7}+\cdots\)
252.4.b.g \(16\) \(14.868\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(3+\beta _{5})q^{4}+\beta _{11}q^{5}+(1+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)