Properties

Label 605.2.u
Level $605$
Weight $2$
Character orbit 605.u
Rep. character $\chi_{605}(4,\cdot)$
Character field $\Q(\zeta_{110})$
Dimension $2560$
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.u (of order \(110\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{110})\)
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 2720 2720 0
Cusp forms 2560 2560 0
Eisenstein series 160 160 0

Trace form

\( 2560q - 144q^{4} - 43q^{5} - 114q^{6} + 534q^{9} + O(q^{10}) \) \( 2560q - 144q^{4} - 43q^{5} - 114q^{6} + 534q^{9} - 22q^{10} - 104q^{11} - 80q^{14} - 58q^{15} - 40q^{16} - 94q^{19} - 32q^{20} - 162q^{21} - 248q^{24} - 25q^{25} - 124q^{26} - 90q^{29} - 103q^{30} - 102q^{31} - 56q^{34} - 66q^{35} - 24q^{36} - 184q^{39} - 45q^{40} - 36q^{41} - 92q^{44} - 2q^{45} - 26q^{46} - 182q^{49} - 94q^{50} + 108q^{51} - 180q^{54} + 52q^{55} + 16q^{56} - 96q^{59} - 63q^{60} - 48q^{61} - 124q^{64} - 37q^{65} - 212q^{66} - 170q^{69} + 30q^{70} - 194q^{71} - 136q^{74} - 46q^{75} - 188q^{76} - 170q^{79} + 65q^{80} - 730q^{81} - 166q^{84} - 58q^{85} - 126q^{86} + 38q^{89} - 144q^{90} - 10q^{91} + 8q^{94} - 180q^{95} - 68q^{96} + 226q^{99} + O(q^{100}) \)

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.u.a \(2560\) \(4.831\) None \(0\) \(0\) \(-43\) \(0\)