Properties

Label 605.2.r
Level $605$
Weight $2$
Character orbit 605.r
Rep. character $\chi_{605}(32,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1280$
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.r (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{44})\)
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 1360 1360 0
Cusp forms 1280 1280 0
Eisenstein series 80 80 0

Trace form

\( 1280q - 22q^{2} - 40q^{3} - 14q^{5} - 44q^{6} - 22q^{7} - 22q^{8} + O(q^{10}) \) \( 1280q - 22q^{2} - 40q^{3} - 14q^{5} - 44q^{6} - 22q^{7} - 22q^{8} - 66q^{10} - 48q^{11} + 44q^{12} - 66q^{13} - 26q^{15} + 80q^{16} - 22q^{17} - 44q^{18} - 54q^{20} - 44q^{21} - 90q^{22} - 34q^{23} - 30q^{25} - 12q^{26} + 80q^{27} - 22q^{28} - 22q^{30} - 52q^{31} - 22q^{32} - 62q^{33} - 22q^{35} + 216q^{36} + 52q^{37} + 70q^{38} - 44q^{41} + 44q^{42} - 22q^{43} + 104q^{45} - 44q^{46} - 18q^{47} - 72q^{48} + 88q^{50} - 484q^{51} - 22q^{52} + 14q^{53} + 140q^{55} - 316q^{56} + 44q^{57} - 6q^{58} + 34q^{60} - 44q^{61} - 22q^{62} - 44q^{63} - 22q^{65} - 84q^{66} - 138q^{67} - 22q^{68} - 126q^{70} - 4q^{71} + 220q^{72} - 22q^{73} - 66q^{75} + 88q^{76} - 22q^{77} - 104q^{78} - 324q^{80} - 1056q^{81} - 58q^{82} - 22q^{83} - 110q^{85} - 52q^{86} + 44q^{87} - 2q^{88} + 176q^{90} + 104q^{91} - 278q^{92} - 128q^{93} - 22q^{95} - 44q^{96} + 46q^{97} - 22q^{98} + O(q^{100}) \)

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.r.a \(1280\) \(4.831\) None \(-22\) \(-40\) \(-14\) \(-22\)