Properties

Label 475.2.r
Level $475$
Weight $2$
Character orbit 475.r
Rep. character $\chi_{475}(11,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $384$
Newform subspaces $1$
Sturm bound $100$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.r (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 475 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 1 \)
Sturm bound: \(100\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(475, [\chi])\).

Total New Old
Modular forms 416 416 0
Cusp forms 384 384 0
Eisenstein series 32 32 0

Trace form

\( 384q - 3q^{2} - 3q^{3} + 43q^{4} - 5q^{5} - 11q^{6} - 28q^{7} - 2q^{8} + 41q^{9} + O(q^{10}) \) \( 384q - 3q^{2} - 3q^{3} + 43q^{4} - 5q^{5} - 11q^{6} - 28q^{7} - 2q^{8} + 41q^{9} - 5q^{10} - 18q^{11} - 32q^{12} - 11q^{13} - 11q^{14} - 21q^{15} + 43q^{16} + 6q^{17} - 48q^{18} - 20q^{20} - 32q^{21} + 19q^{22} + 11q^{23} - 7q^{25} - 60q^{26} - 6q^{27} - 25q^{28} - 21q^{29} + 4q^{30} + 12q^{31} + 14q^{32} + 9q^{33} - 19q^{34} - 27q^{35} + 19q^{36} - 28q^{37} + q^{38} - 12q^{40} - 19q^{41} - 73q^{42} - 54q^{43} + 31q^{44} - 52q^{45} - 52q^{46} + 25q^{47} + 31q^{48} + 276q^{49} + 46q^{50} + 54q^{51} - 57q^{52} + 15q^{53} - 20q^{54} + 20q^{55} - 36q^{56} - 152q^{57} - 122q^{58} - 51q^{59} - 34q^{60} - 17q^{61} - 6q^{62} + 27q^{63} - 114q^{64} - 160q^{65} + 5q^{66} + 81q^{67} + 124q^{68} - 48q^{70} - 44q^{71} - 112q^{72} + 41q^{73} + 10q^{74} + 56q^{75} - 84q^{76} - 12q^{77} + 52q^{78} - 19q^{79} - 75q^{80} + 123q^{81} + 42q^{82} - 50q^{83} - 252q^{84} - 8q^{85} - 41q^{86} - 34q^{87} + 132q^{88} - 21q^{89} - 9q^{90} - 40q^{91} - 75q^{92} + 242q^{93} + 16q^{94} - 48q^{95} + 126q^{96} - 4q^{97} - 58q^{98} + 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
475.2.r.a \(384\) \(3.793\) None \(-3\) \(-3\) \(-5\) \(-28\)