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Properties

Label 600.2.bq
Level $600$
Weight $2$
Character orbit 600.bq
Rep. character $\chi_{600}(67,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
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.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
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 992 480 512
Cusp forms 928 480 448
Eisenstein series 64 0 64

Trace form

\( 480 q + 12 q^{8} + O(q^{10}) \) \( 480 q + 12 q^{8} - 8 q^{10} + 8 q^{12} - 8 q^{17} + 20 q^{20} + 28 q^{22} + 8 q^{25} - 4 q^{28} - 8 q^{30} - 20 q^{32} + 48 q^{35} + 20 q^{38} - 108 q^{40} - 20 q^{42} + 32 q^{43} - 140 q^{44} - 16 q^{48} + 124 q^{50} - 132 q^{52} + 152 q^{58} - 20 q^{60} + 116 q^{62} - 60 q^{64} + 8 q^{65} - 48 q^{67} - 72 q^{68} - 4 q^{70} - 12 q^{72} + 40 q^{73} + 24 q^{78} - 76 q^{80} + 120 q^{81} - 64 q^{82} - 80 q^{83} - 80 q^{84} - 132 q^{88} + 200 q^{89} - 48 q^{90} - 216 q^{92} - 40 q^{94} + 20 q^{96} - 56 q^{97} - 192 q^{98} + O(q^{100}) \)

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.bq.a 600.bq 200.v $480$ $4.791$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$

Decomposition of \(S_{2}^{\mathrm{old}}(600, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(600, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 2}\)