Properties

Label 177.8.a
Level $177$
Weight $8$
Character orbit 177.a
Rep. character $\chi_{177}(1,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $4$
Sturm bound $160$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 177.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(177))\).

Total New Old
Modular forms 142 68 74
Cusp forms 138 68 70
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
\(+\)\(+\)$+$\(17\)
\(+\)\(-\)$-$\(16\)
\(-\)\(+\)$-$\(17\)
\(-\)\(-\)$+$\(18\)
Plus space\(+\)\(35\)
Minus space\(-\)\(33\)

Trace form

\( 68 q - 12 q^{2} + 54 q^{3} + 4664 q^{4} - 780 q^{5} - 108 q^{6} + 1476 q^{7} + 636 q^{8} + 49572 q^{9} + O(q^{10}) \) \( 68 q - 12 q^{2} + 54 q^{3} + 4664 q^{4} - 780 q^{5} - 108 q^{6} + 1476 q^{7} + 636 q^{8} + 49572 q^{9} + 260 q^{10} + 5316 q^{11} + 10368 q^{12} + 10980 q^{13} - 17836 q^{14} - 216 q^{15} + 342072 q^{16} - 24740 q^{17} - 8748 q^{18} - 2860 q^{19} - 452 q^{20} - 3456 q^{21} - 176024 q^{22} - 58976 q^{23} - 154224 q^{24} + 984900 q^{25} - 651436 q^{26} + 39366 q^{27} - 172016 q^{28} - 311120 q^{29} - 157248 q^{30} - 604 q^{31} + 88436 q^{32} + 190296 q^{33} - 797944 q^{34} + 639040 q^{35} + 3400056 q^{36} - 710260 q^{37} - 1040284 q^{38} - 244620 q^{39} + 1802580 q^{40} + 941432 q^{41} + 660096 q^{42} - 637056 q^{43} + 581340 q^{44} - 568620 q^{45} - 968020 q^{46} - 678428 q^{47} + 1548288 q^{48} + 9776792 q^{49} + 5008484 q^{50} + 2598588 q^{51} + 1732552 q^{52} - 2867372 q^{53} - 78732 q^{54} - 39700 q^{55} - 8128156 q^{56} - 722304 q^{57} - 2710396 q^{58} - 7106616 q^{60} + 5017912 q^{61} - 6064920 q^{62} + 1076004 q^{63} + 33042748 q^{64} + 2940020 q^{65} + 1999512 q^{66} - 5304496 q^{67} + 374168 q^{68} - 4885812 q^{69} - 3642996 q^{70} - 4243764 q^{71} + 463644 q^{72} - 16338872 q^{73} + 5064880 q^{74} + 245754 q^{75} - 12737280 q^{76} + 29922972 q^{77} + 9269532 q^{78} + 12391120 q^{79} - 29375296 q^{80} + 36137988 q^{81} - 2566284 q^{82} + 13277628 q^{83} - 20585016 q^{84} - 9427828 q^{85} + 32532232 q^{86} + 10963080 q^{87} - 20176068 q^{88} + 4515288 q^{89} + 189540 q^{90} + 2409016 q^{91} - 13373644 q^{92} - 11127996 q^{93} - 18354768 q^{94} - 19264308 q^{95} + 17514900 q^{96} - 12947124 q^{97} - 22197832 q^{98} + 3875364 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(177))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 59
177.8.a.a 177.a 1.a $16$ $55.292$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(-432\) \(-68\) \(-2343\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3^{3}q^{3}+(61+\beta _{2})q^{4}+(-5+\cdots)q^{5}+\cdots\)
177.8.a.b 177.a 1.a $17$ $55.292$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-32\) \(459\) \(-1072\) \(-2407\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-2+\beta _{1})q^{2}+3^{3}q^{3}+(69-3\beta _{1}+\cdots)q^{4}+\cdots\)
177.8.a.c 177.a 1.a $17$ $55.292$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(2\) \(-459\) \(-318\) \(3145\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3^{3}q^{3}+(68+\beta _{1}+\beta _{2})q^{4}+\cdots\)
177.8.a.d 177.a 1.a $18$ $55.292$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(24\) \(486\) \(678\) \(3081\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+3^{3}q^{3}+(75+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(177))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(177)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 2}\)