↑

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 $1$

Related objects

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
177.4.d.a 177.d 177.d $2$ $10.443$ \(\Q(\sqrt{-59}) \) \(\Q(\sqrt{-59}) \) \(0\) \(7\) \(0\) \(58\) $\mathrm{U}(1)[D_{2}]$ \(q+(4-\beta )q^{3}-8q^{4}+(-1+2\beta )q^{5}+\cdots\)
177.4.d.b 177.d 177.d $4$ $10.443$ \(\Q(\sqrt{-3}, \sqrt{-59})\) \(\Q(\sqrt{-59}) \) \(0\) \(-7\) \(0\) \(-58\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2-\beta _{2}-\beta _{3})q^{3}-8q^{4}+(4\beta _{1}+\cdots)q^{5}+\cdots\)
177.4.d.c 177.d 177.d $52$ $10.443$ None \(0\) \(-8\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$