Properties

Label 847.2.ba
Level $847$
Weight $2$
Character orbit 847.ba
Rep. character $\chi_{847}(6,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $3440$
Newform subspaces $2$
Sturm bound $176$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 847 = 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 847.ba (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 847 \)
Character field: \(\Q(\zeta_{110})\)
Newform subspaces: \( 2 \)
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 3600 3600 0
Cusp forms 3440 3440 0
Eisenstein series 160 160 0

Trace form

\( 3440q - 78q^{2} - 168q^{4} - 34q^{7} - 88q^{8} + 754q^{9} + O(q^{10}) \) \( 3440q - 78q^{2} - 168q^{4} - 34q^{7} - 88q^{8} + 754q^{9} - 64q^{11} - 13q^{14} - 176q^{15} - 10q^{16} - 75q^{18} - 77q^{21} - 160q^{22} - 118q^{23} - 128q^{25} - 69q^{28} - 98q^{29} - 114q^{30} - 88q^{32} - 84q^{35} - 16q^{36} - 132q^{37} - 184q^{39} - 121q^{42} - 88q^{43} - 92q^{44} - 93q^{46} - 16q^{49} - 28q^{50} - 232q^{51} - 78q^{53} + 26q^{56} - 64q^{57} - 164q^{58} - 262q^{60} - 35q^{63} - 178q^{64} - 88q^{65} - 88q^{67} - 56q^{70} + 67q^{72} - 178q^{74} + 100q^{77} - 198q^{78} - 10q^{79} - 862q^{81} - 7q^{84} - 278q^{85} - 117q^{86} - 16q^{88} - 55q^{91} - 597q^{92} - 56q^{93} - 116q^{95} - 132q^{98} - 150q^{99} + O(q^{100}) \)

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.ba.a \(80\) \(6.763\) \(\Q(\sqrt{-7}) \) \(0\) \(0\) \(0\) \(0\)
847.2.ba.b \(3360\) \(6.763\) None \(-78\) \(0\) \(0\) \(-34\)