Properties

Label 483.2.y
Level $483$
Weight $2$
Character orbit 483.y
Rep. character $\chi_{483}(4,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $640$
Newform subspaces $2$
Sturm bound $128$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.y (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Newform subspaces: \( 2 \)
Sturm bound: \(128\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 1360 640 720
Cusp forms 1200 640 560
Eisenstein series 160 0 160

Trace form

\( 640q + 4q^{2} + 36q^{4} - 4q^{5} + 4q^{7} - 24q^{8} + 32q^{9} + O(q^{10}) \) \( 640q + 4q^{2} + 36q^{4} - 4q^{5} + 4q^{7} - 24q^{8} + 32q^{9} + 8q^{10} - 4q^{11} + 8q^{14} + 8q^{17} + 4q^{18} + 8q^{19} - 144q^{20} - 32q^{22} - 44q^{23} - 28q^{26} + 132q^{28} - 40q^{29} - 8q^{30} - 4q^{31} - 36q^{32} + 8q^{33} + 16q^{34} - 44q^{35} - 28q^{36} - 28q^{37} - 196q^{38} + 36q^{40} + 32q^{41} - 106q^{42} + 80q^{43} - 146q^{44} - 4q^{45} - 4q^{47} + 32q^{48} - 72q^{49} + 356q^{50} - 44q^{51} - 216q^{52} + 24q^{53} + 32q^{55} - 102q^{56} + 72q^{57} + 14q^{58} - 92q^{59} - 20q^{60} - 52q^{61} - 96q^{62} + 4q^{63} - 168q^{64} - 40q^{65} + 16q^{66} + 12q^{68} + 16q^{69} - 72q^{70} + 16q^{71} + 12q^{72} - 24q^{73} + 2q^{74} - 16q^{75} - 32q^{76} + 8q^{77} + 52q^{79} + 122q^{80} + 32q^{81} - 152q^{82} - 80q^{83} - 8q^{84} - 368q^{85} + 64q^{86} - 12q^{87} - 250q^{88} + 32q^{89} - 16q^{90} + 56q^{91} - 396q^{92} + 24q^{93} + 194q^{94} - 134q^{95} - 20q^{96} - 16q^{97} - 56q^{98} - 36q^{99} + O(q^{100}) \)

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.y.a \(320\) \(3.857\) None \(2\) \(-16\) \(-2\) \(2\)
483.2.y.b \(320\) \(3.857\) None \(2\) \(16\) \(-2\) \(2\)

Decomposition of \(S_{2}^{\mathrm{old}}(483, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(483, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)