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Properties

Label 483.2.bf
Level $483$
Weight $2$
Character orbit 483.bf
Rep. character $\chi_{483}(10,\cdot)$
Character field $\Q(\zeta_{66})$
Dimension $640$
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.bf (of order \(66\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
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 640 720
Cusp forms 1200 640 560
Eisenstein series 160 0 160

Trace form

\( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + O(q^{10}) \) \( 640 q - 4 q^{2} + 36 q^{4} + 24 q^{8} - 32 q^{9} + 4 q^{18} - 28 q^{23} + 56 q^{25} - 84 q^{26} - 176 q^{28} - 24 q^{29} + 12 q^{31} + 36 q^{32} - 76 q^{35} + 28 q^{36} + 44 q^{37} - 110 q^{42} - 88 q^{43} + 154 q^{44} + 8 q^{46} + 12 q^{47} - 8 q^{49} - 212 q^{50} + 44 q^{51} + 108 q^{52} - 110 q^{56} - 88 q^{57} + 2 q^{58} - 36 q^{59} - 168 q^{64} - 48 q^{70} + 16 q^{71} + 12 q^{72} - 48 q^{73} - 22 q^{74} + 48 q^{75} + 32 q^{78} - 44 q^{79} - 594 q^{80} + 32 q^{81} + 24 q^{82} + 352 q^{85} - 36 q^{87} - 330 q^{88} + 244 q^{92} - 24 q^{93} - 486 q^{94} - 154 q^{95} - 60 q^{96} - 24 q^{98} - 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
483.2.bf.a 483.bf 161.o $640$ $3.857$ None 483.2.bf.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{66}]$

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

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