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Properties

Label 605.2.o
Level $605$
Weight $2$
Character orbit 605.o
Rep. character $\chi_{605}(34,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $640$
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.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
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 680 680 0
Cusp forms 640 640 0
Eisenstein series 40 40 0

Trace form

\( 640q + 44q^{4} - 7q^{5} + 14q^{6} - 644q^{9} + O(q^{10}) \) \( 640q + 44q^{4} - 7q^{5} + 14q^{6} - 644q^{9} - 23q^{10} + 4q^{11} - 30q^{14} + 18q^{15} - 100q^{16} - 6q^{19} - 3q^{20} + 32q^{21} + 128q^{24} - 15q^{25} - 26q^{26} - 10q^{29} + 28q^{30} - 18q^{31} - 34q^{34} - 29q^{35} - 66q^{36} + 44q^{39} - 50q^{40} - 34q^{41} - 28q^{44} - 43q^{45} - 14q^{46} + 102q^{49} + 29q^{50} - 148q^{51} + 90q^{54} - 102q^{55} - 106q^{56} - 34q^{59} + 58q^{60} - 42q^{61} + 24q^{64} + 22q^{65} + 52q^{66} + 20q^{69} - 75q^{70} + 54q^{71} - 34q^{74} - 4q^{75} - 2q^{76} + 50q^{79} - 160q^{80} + 560q^{81} - 4q^{84} - 57q^{85} + 6q^{86} - 128q^{89} + 39q^{90} - 80q^{91} - 88q^{94} + 65q^{95} + 8q^{96} - 266q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.o.a \(640\) \(4.831\) None \(0\) \(0\) \(-7\) \(0\)