Properties

Label 847.2.i
Level $847$
Weight $2$
Character orbit 847.i
Rep. character $\chi_{847}(241,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $128$
Newform subspaces $3$
Sturm bound $176$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.i (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(176\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 200 160 40
Cusp forms 152 128 24
Eisenstein series 48 32 16

Trace form

\( 128q + 6q^{3} + 56q^{4} + 54q^{9} + O(q^{10}) \) \( 128q + 6q^{3} + 56q^{4} + 54q^{9} - 12q^{12} - 16q^{14} + 20q^{15} - 56q^{16} + 10q^{23} + 16q^{25} - 78q^{26} - 6q^{31} + 32q^{36} - 12q^{37} + 78q^{38} - 64q^{42} - 84q^{45} + 24q^{47} - 10q^{49} - 44q^{56} + 22q^{58} - 12q^{59} - 52q^{60} - 20q^{64} + 8q^{67} + 38q^{70} - 4q^{71} + 102q^{75} - 76q^{78} - 54q^{80} + 4q^{81} - 78q^{82} + 50q^{86} + 42q^{89} + 50q^{91} - 40q^{92} + 16q^{93} + O(q^{100}) \)

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.i.a \(24\) \(6.763\) None \(0\) \(0\) \(0\) \(0\)
847.2.i.b \(48\) \(6.763\) None \(0\) \(6\) \(0\) \(0\)
847.2.i.c \(56\) \(6.763\) None \(0\) \(0\) \(0\) \(0\)

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

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