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Properties

Label 600.2.bg
Level $600$
Weight $2$
Character orbit 600.bg
Rep. character $\chi_{600}(11,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $464$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 600.bg (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 600 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(600, [\chi])\).

Total New Old
Modular forms 496 496 0
Cusp forms 464 464 0
Eisenstein series 32 32 0

Trace form

\( 464 q - 6 q^{3} - 6 q^{4} - 7 q^{6} - 6 q^{9} + O(q^{10}) \) \( 464 q - 6 q^{3} - 6 q^{4} - 7 q^{6} - 6 q^{9} - 8 q^{10} + 3 q^{12} + 6 q^{16} + 2 q^{18} - 12 q^{19} - 22 q^{22} - 16 q^{25} - 6 q^{27} + 34 q^{28} + 3 q^{30} - 18 q^{33} - 30 q^{34} + 35 q^{36} + 4 q^{40} + 43 q^{42} + 22 q^{46} - 50 q^{48} - 400 q^{49} - 28 q^{51} + 32 q^{54} - 4 q^{57} + 54 q^{58} - 76 q^{60} - 30 q^{64} - 58 q^{66} - 12 q^{67} + 48 q^{70} - 69 q^{72} - 12 q^{73} - 30 q^{75} + 48 q^{76} - 79 q^{78} - 6 q^{81} + 12 q^{82} - 22 q^{84} - 130 q^{88} - 48 q^{90} + 72 q^{91} - 72 q^{94} + 44 q^{96} - 36 q^{97} - 52 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(600, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
600.2.bg.a 600.bg 600.ag $464$ $4.791$ None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$