Properties

Label 483.2.bc
Level $483$
Weight $2$
Character orbit 483.bc
Rep. character $\chi_{483}(11,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $1200$
Newform subspaces $1$
Sturm bound $128$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.bc (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 483 \)
Character field: \(\Q(\zeta_{66})\)
Newform subspaces: \( 1 \)
Sturm bound: \(128\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(483, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1200 1200 0
Eisenstein series 160 160 0

Trace form

\( 1200q - 9q^{3} - 74q^{4} - 20q^{6} - 44q^{7} - 13q^{9} + O(q^{10}) \) \( 1200q - 9q^{3} - 74q^{4} - 20q^{6} - 44q^{7} - 13q^{9} - 22q^{10} - 25q^{12} - 72q^{13} - 44q^{15} + 38q^{16} - 45q^{18} - 22q^{19} + 44q^{21} + 2q^{24} + 18q^{25} - 90q^{27} - 44q^{28} - 55q^{30} - 18q^{31} - 11q^{33} - 88q^{34} - 108q^{36} - 66q^{37} + q^{39} - 22q^{40} - 22q^{42} - 2q^{46} - 228q^{48} - 128q^{49} - 11q^{51} - 166q^{52} + 35q^{54} - 160q^{55} - 44q^{57} - 126q^{58} - 11q^{60} + 66q^{61} + 33q^{63} + 40q^{64} + 22q^{66} - 22q^{67} - 24q^{69} + 68q^{70} - 149q^{72} - 42q^{73} + 123q^{75} - 88q^{76} - 108q^{78} - 66q^{79} - 81q^{81} - 14q^{82} + 44q^{84} - 200q^{85} + 75q^{87} + 66q^{88} + 16q^{93} - 146q^{94} + 5q^{96} - 88q^{97} - 308q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(483, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
483.2.bc.a \(1200\) \(3.857\) None \(0\) \(-9\) \(0\) \(-44\)