Properties

Label 177.4.d
Level $177$
Weight $4$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $3$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(177, [\chi])\).

Total New Old
Modular forms 62 62 0
Cusp forms 58 58 0
Eisenstein series 4 4 0

Trace form

\( 58q - 8q^{3} + 220q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 58q - 8q^{3} + 220q^{4} - 16q^{7} - 4q^{9} + 28q^{12} - 18q^{15} + 868q^{16} - 184q^{19} - 188q^{21} - 60q^{22} - 714q^{25} + 70q^{27} - 4q^{28} - 888q^{36} + 1864q^{45} - 660q^{46} - 488q^{48} + 1134q^{49} - 1772q^{51} - 708q^{57} - 824q^{60} - 2288q^{63} + 4576q^{64} + 1316q^{66} + 2308q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} - 3332q^{84} - 848q^{85} + 2170q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.4.d.a \(2\) \(10.443\) \(\Q(\sqrt{-59}) \) \(\Q(\sqrt{-59}) \) \(0\) \(7\) \(0\) \(58\) \(q+(4-\beta )q^{3}-8q^{4}+(-1+2\beta )q^{5}+\cdots\)
177.4.d.b \(4\) \(10.443\) \(\Q(\sqrt{-3}, \sqrt{-59})\) \(\Q(\sqrt{-59}) \) \(0\) \(-7\) \(0\) \(-58\) \(q+(-2-\beta _{2}-\beta _{3})q^{3}-8q^{4}+(4\beta _{1}+\cdots)q^{5}+\cdots\)
177.4.d.c \(52\) \(10.443\) None \(0\) \(-8\) \(0\) \(-16\)