Properties

Label 605.2.w
Level $605$
Weight $2$
Character orbit 605.w
Rep. character $\chi_{605}(2,\cdot)$
Character field $\Q(\zeta_{220})$
Dimension $5120$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.w (of order \(220\) and degree \(80\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{220})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

Total New Old
Modular forms 5440 5440 0
Cusp forms 5120 5120 0
Eisenstein series 320 320 0

Trace form

\( 5120q - 78q^{2} - 60q^{3} - 86q^{5} - 156q^{6} - 88q^{7} - 78q^{8} + O(q^{10}) \) \( 5120q - 78q^{2} - 60q^{3} - 86q^{5} - 156q^{6} - 88q^{7} - 78q^{8} - 44q^{10} - 152q^{11} - 134q^{12} - 34q^{13} - 94q^{15} - 280q^{16} - 88q^{17} - 56q^{18} - 96q^{20} - 176q^{21} - 10q^{22} - 56q^{23} - 110q^{25} - 188q^{26} - 180q^{27} - 138q^{28} - 118q^{30} - 148q^{31} - 88q^{32} - 88q^{33} - 78q^{35} - 496q^{36} - 152q^{37} - 230q^{38} - 60q^{40} - 216q^{41} - 144q^{42} - 88q^{43} - 194q^{45} - 236q^{46} - 52q^{47} + 12q^{48} - 148q^{50} + 244q^{51} - 38q^{52} - 84q^{53} - 200q^{55} + 136q^{56} - 184q^{57} - 14q^{58} - 114q^{60} - 116q^{61} - 188q^{62} - 36q^{63} - 88q^{65} - 76q^{66} + 48q^{67} - 58q^{68} - 14q^{70} - 196q^{71} - 410q^{72} - 138q^{73} - 114q^{75} - 308q^{76} - 158q^{77} + 14q^{78} + 124q^{80} + 836q^{81} - 82q^{82} - 178q^{83} - 30q^{85} - 268q^{86} - 154q^{87} - 258q^{88} - 266q^{90} - 344q^{91} + 188q^{92} - 32q^{93} - 48q^{95} - 176q^{96} - 86q^{97} - 88q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
605.2.w.a \(5120\) \(4.831\) None \(-78\) \(-60\) \(-86\) \(-88\)