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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.6.d.a 177.d 177.d $6$ $28.388$ 6.0.149721291.1 \(\Q(\sqrt{-59}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(4\beta _{2}+3\beta _{3}-3\beta _{4})q^{3}-2^{5}q^{4}+(21\beta _{1}+\cdots)q^{5}+\cdots\)
177.6.d.b 177.d 177.d $92$ $28.388$ None \(0\) \(22\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{2}]$