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Properties

Label 650.2.bh
Level $650$
Weight $2$
Character orbit 650.bh
Rep. character $\chi_{650}(121,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $272$
Newform subspaces $1$
Sturm bound $210$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.bh (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 325 \)
Character field: \(\Q(\zeta_{30})\)
Newform subspaces: \( 1 \)
Sturm bound: \(210\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(650, [\chi])\).

Total New Old
Modular forms 880 272 608
Cusp forms 816 272 544
Eisenstein series 64 0 64

Trace form

\( 272 q - 34 q^{4} + 30 q^{9} + O(q^{10}) \) \( 272 q - 34 q^{4} + 30 q^{9} - 2 q^{10} - 12 q^{13} + 16 q^{14} - 12 q^{15} + 34 q^{16} + 20 q^{23} - 28 q^{25} - 4 q^{26} - 24 q^{27} - 28 q^{29} - 4 q^{30} + 6 q^{35} - 30 q^{36} - 18 q^{37} + 24 q^{38} + 28 q^{39} - 4 q^{40} - 42 q^{41} + 12 q^{42} + 104 q^{49} + 48 q^{51} + 32 q^{53} - 36 q^{54} - 42 q^{55} + 8 q^{56} - 12 q^{58} - 36 q^{59} - 12 q^{61} + 36 q^{62} - 138 q^{63} + 68 q^{64} - 56 q^{65} + 32 q^{66} - 24 q^{67} + 66 q^{69} - 24 q^{72} + 76 q^{74} + 10 q^{75} - 216 q^{77} - 2 q^{78} - 16 q^{79} + 38 q^{81} + 80 q^{82} + 36 q^{85} + 56 q^{87} - 90 q^{89} - 56 q^{90} - 68 q^{91} - 40 q^{92} - 36 q^{93} + 40 q^{95} - 36 q^{97} - 72 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(650, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
650.2.bh.a 650.bh 325.ag $272$ $5.190$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{30}]$

Decomposition of \(S_{2}^{\mathrm{old}}(650, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)