Properties

Label 177.6.d
Level $177$
Weight $6$
Character orbit 177.d
Rep. character $\chi_{177}(176,\cdot)$
Character field $\Q$
Dimension $98$
Newform subspaces $2$
Sturm bound $120$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 177 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(177, [\chi])\).

Total New Old
Modular forms 102 102 0
Cusp forms 98 98 0
Eisenstein series 4 4 0

Trace form

\( 98q + 22q^{3} + 1532q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \) \( 98q + 22q^{3} + 1532q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 4269q^{15} + 20868q^{16} + 1784q^{19} + 3313q^{21} - 8140q^{22} - 66958q^{25} - 18407q^{27} - 19092q^{28} - 20832q^{36} - 53837q^{45} + 51180q^{46} + 61720q^{48} + 275398q^{49} + 8332q^{51} + 105783q^{57} + 274312q^{60} - 249158q^{63} + 364864q^{64} - 11596q^{66} - 27356q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 367708q^{84} + 111028q^{85} - 96965q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.6.d.a \(6\) \(28.388\) 6.0.149721291.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) \(q+(4\beta _{2}+3\beta _{3}-3\beta _{4})q^{3}-2^{5}q^{4}+(21\beta _{1}+\cdots)q^{5}+\cdots\)
177.6.d.b \(92\) \(28.388\) None \(0\) \(22\) \(0\) \(-80\)