Properties

Label 177.2.e
Level $177$
Weight $2$
Character orbit 177.e
Rep. character $\chi_{177}(4,\cdot)$
Character field $\Q(\zeta_{29})$
Dimension $280$
Newform subspaces $2$
Sturm bound $40$
Trace bound $2$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 177.e (of order \(29\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{29})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(177, [\chi])\).

Total New Old
Modular forms 616 280 336
Cusp forms 504 280 224
Eisenstein series 112 0 112

Trace form

\( 280q - 10q^{4} - 2q^{6} - 4q^{7} - 12q^{8} - 10q^{9} + O(q^{10}) \) \( 280q - 10q^{4} - 2q^{6} - 4q^{7} - 12q^{8} - 10q^{9} - 28q^{10} - 12q^{11} - 8q^{12} - 8q^{13} - 44q^{14} - 4q^{15} - 34q^{16} - 16q^{17} - 12q^{19} - 28q^{20} - 20q^{22} - 16q^{23} - 6q^{24} - 30q^{25} - 44q^{26} - 60q^{28} - 28q^{29} - 28q^{30} - 36q^{31} - 44q^{32} - 16q^{33} - 56q^{34} - 64q^{35} - 10q^{36} - 16q^{37} - 92q^{38} - 16q^{39} - 116q^{40} - 44q^{41} - 16q^{42} - 56q^{43} - 84q^{44} + 48q^{46} + 6q^{47} - 48q^{48} + 30q^{49} + 176q^{50} - 16q^{51} + 180q^{52} + 52q^{53} - 2q^{54} + 98q^{55} + 324q^{56} - 8q^{57} + 8q^{58} + 56q^{59} - 36q^{60} + 56q^{61} + 44q^{62} - 4q^{63} + 346q^{64} + 82q^{65} - 32q^{66} + 28q^{67} + 104q^{68} - 28q^{69} + 92q^{70} + 8q^{71} - 12q^{72} - 26q^{73} + 28q^{74} - 32q^{75} - 104q^{76} - 108q^{77} - 68q^{78} - 80q^{79} - 152q^{80} - 10q^{81} - 180q^{82} - 84q^{83} - 40q^{84} - 68q^{85} - 136q^{86} - 20q^{87} - 144q^{88} - 60q^{89} - 28q^{90} - 120q^{91} - 164q^{92} - 12q^{93} - 168q^{94} - 108q^{95} - 34q^{96} - 104q^{97} - 14q^{98} - 12q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(177, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
177.2.e.a \(140\) \(1.413\) None \(-1\) \(-5\) \(-2\) \(-2\)
177.2.e.b \(140\) \(1.413\) None \(1\) \(5\) \(2\) \(-2\)

Decomposition of \(S_{2}^{\mathrm{old}}(177, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(177, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(59, [\chi])\)\(^{\oplus 2}\)