Properties

Label 155.2.n
Level $155$
Weight $2$
Character orbit 155.n
Rep. character $\chi_{155}(4,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $56$
Newform subspaces $1$
Sturm bound $32$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 155 = 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 155.n (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 155 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(32\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

Total New Old
Modular forms 72 72 0
Cusp forms 56 56 0
Eisenstein series 16 16 0

Trace form

\( 56q + 2q^{4} - 10q^{5} - 4q^{6} + 8q^{9} + O(q^{10}) \) \( 56q + 2q^{4} - 10q^{5} - 4q^{6} + 8q^{9} + 4q^{10} - 14q^{11} - 16q^{14} + 21q^{15} - 22q^{16} - 2q^{19} - 29q^{20} - 38q^{21} - 30q^{24} - 10q^{25} + 12q^{26} + 20q^{29} - 30q^{30} + 26q^{31} - 2q^{34} + 24q^{35} - 44q^{36} - 18q^{39} + 36q^{40} - 20q^{41} + 62q^{44} + 8q^{45} - 70q^{46} - 42q^{49} - 11q^{50} + 10q^{51} - 26q^{54} - 30q^{55} + 208q^{56} - 50q^{59} - 67q^{60} + 56q^{61} + 12q^{64} - 27q^{65} + 60q^{66} + 34q^{69} + 5q^{70} - 8q^{71} - 84q^{74} - 38q^{75} - 20q^{76} + 122q^{79} - 80q^{80} + 42q^{81} - 40q^{84} - 18q^{85} + 78q^{86} - 28q^{89} + 144q^{90} - 20q^{91} + 160q^{94} + 9q^{95} - 70q^{96} - 52q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
155.2.n.a \(56\) \(1.238\) None \(0\) \(0\) \(-10\) \(0\)