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Properties

Label 177.6.a
Level $177$
Weight $6$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $4$
Sturm bound $120$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(120\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(177))\).

Total New Old
Modular forms 102 48 54
Cusp forms 98 48 50
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(59\)FrickeDim.
\(+\)\(+\)\(+\)\(12\)
\(+\)\(-\)\(-\)\(13\)
\(-\)\(+\)\(-\)\(12\)
\(-\)\(-\)\(+\)\(11\)
Plus space\(+\)\(23\)
Minus space\(-\)\(25\)

Trace form

\( 48q + 12q^{2} - 18q^{3} + 792q^{4} - 12q^{5} + 180q^{6} + 4q^{7} + 156q^{8} + 3888q^{9} + O(q^{10}) \) \( 48q + 12q^{2} - 18q^{3} + 792q^{4} - 12q^{5} + 180q^{6} + 4q^{7} + 156q^{8} + 3888q^{9} - 524q^{10} + 1524q^{11} - 864q^{12} - 1004q^{13} - 2156q^{14} - 504q^{15} + 11000q^{16} - 4420q^{17} + 972q^{18} - 2332q^{19} - 9316q^{20} + 720q^{21} - 12904q^{22} + 1280q^{23} + 432q^{24} + 41768q^{25} + 5956q^{26} - 1458q^{27} + 16560q^{28} - 18040q^{29} + 8352q^{30} + 15812q^{31} - 2156q^{32} + 360q^{33} + 3160q^{34} - 3712q^{35} + 64152q^{36} + 4844q^{37} + 29668q^{38} - 10476q^{39} - 22092q^{40} + 32608q^{41} + 8352q^{42} - 33344q^{43} + 18204q^{44} - 972q^{45} - 36692q^{46} - 8860q^{47} - 32256q^{48} + 80812q^{49} - 85172q^{50} - 18324q^{51} + 31560q^{52} - 9964q^{53} + 14580q^{54} + 56812q^{55} - 60860q^{56} + 24336q^{57} - 122348q^{58} + 30024q^{60} - 79920q^{61} + 232776q^{62} + 324q^{63} + 214204q^{64} - 73796q^{65} - 86760q^{66} - 28336q^{67} - 316328q^{68} - 12924q^{69} + 128556q^{70} - 17556q^{71} + 12636q^{72} + 164832q^{73} + 168032q^{74} - 59886q^{75} - 99872q^{76} - 290508q^{77} - 73044q^{78} - 307920q^{79} + 69856q^{80} + 314928q^{81} + 295140q^{82} - 333972q^{83} + 135432q^{84} - 207884q^{85} + 131048q^{86} + 64008q^{87} - 376260q^{88} - 126816q^{89} - 42444q^{90} - 84968q^{91} - 77420q^{92} - 103716q^{93} - 210576q^{94} - 174036q^{95} - 47916q^{96} - 158084q^{97} + 905776q^{98} + 123444q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 59
177.6.a.a \(11\) \(28.388\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-6\) \(99\) \(-192\) \(-371\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{2}+9q^{3}+(14-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.6.a.b \(12\) \(28.388\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-108\) \(36\) \(-411\) \(+\) \(+\) \(q-\beta _{1}q^{2}-9q^{3}+(17+\beta _{2})q^{4}+(3+\beta _{1}+\cdots)q^{5}+\cdots\)
177.6.a.c \(12\) \(28.388\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(22\) \(108\) \(158\) \(413\) \(-\) \(+\) \(q+(2-\beta _{1})q^{2}+9q^{3}+(17-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
177.6.a.d \(13\) \(28.388\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(0\) \(-117\) \(-14\) \(373\) \(+\) \(-\) \(q+\beta _{1}q^{2}-9q^{3}+(19+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)