Properties

Label 177.5.c
Level $177$
Weight $5$
Character orbit 177.c
Rep. character $\chi_{177}(58,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $100$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(100\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(177, [\chi])\).

Total New Old
Modular forms 82 40 42
Cusp forms 78 40 38
Eisenstein series 4 0 4

Trace form

\( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.5.c.a \(40\) \(18.296\) None \(0\) \(0\) \(0\) \(80\)

Decomposition of \(S_{5}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)