Properties

Label 847.2.b
Level $847$
Weight $2$
Character orbit 847.b
Rep. character $\chi_{847}(846,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $6$
Sturm bound $176$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(176\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(847, [\chi])\).

Total New Old
Modular forms 100 80 20
Cusp forms 76 64 12
Eisenstein series 24 16 8

Trace form

\( 64q - 50q^{4} - 48q^{9} + O(q^{10}) \) \( 64q - 50q^{4} - 48q^{9} - 2q^{14} - 20q^{15} + 26q^{16} + 8q^{23} - 40q^{25} + 70q^{36} + 24q^{37} + 16q^{42} + 28q^{49} - 24q^{53} - 82q^{56} - 52q^{58} - 68q^{60} + 86q^{64} - 68q^{67} + 28q^{70} - 20q^{71} + 76q^{78} + 8q^{81} + 4q^{86} + 76q^{91} - 20q^{92} + 20q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(847, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
847.2.b.a \(8\) \(6.763\) 8.0.\(\cdots\).11 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{2}+\beta _{4})q^{2}-\beta _{3}q^{3}+(-2+\beta _{6}+\cdots)q^{4}+\cdots\)
847.2.b.b \(8\) \(6.763\) 8.0.37515625.1 \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
847.2.b.c \(8\) \(6.763\) 8.0.4956160000.2 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+\beta _{6}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
847.2.b.d \(8\) \(6.763\) 8.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{6}q^{2}-\beta _{1}q^{4}+\beta _{7}q^{5}+(-\beta _{3}-\beta _{5}+\cdots)q^{7}+\cdots\)
847.2.b.e \(16\) \(6.763\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{3}+\beta _{10})q^{2}+(-\beta _{5}+\beta _{14}+\beta _{15})q^{3}+\cdots\)
847.2.b.f \(16\) \(6.763\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{5})q^{2}-\beta _{14}q^{3}+(1-\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(847, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(847, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)