Properties

Label 650.2.b
Level $650$
Weight $2$
Character orbit 650.b
Rep. character $\chi_{650}(599,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $9$
Sturm bound $210$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 650.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(210\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

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

Total New Old
Modular forms 118 18 100
Cusp forms 94 18 76
Eisenstein series 24 0 24

Trace form

\( 18 q - 18 q^{4} + 4 q^{6} - 18 q^{9} + O(q^{10}) \) \( 18 q - 18 q^{4} + 4 q^{6} - 18 q^{9} - 12 q^{11} - 8 q^{14} + 18 q^{16} + 4 q^{19} - 16 q^{21} - 4 q^{24} - 6 q^{26} - 16 q^{29} - 16 q^{31} + 8 q^{34} + 18 q^{36} + 8 q^{41} + 12 q^{44} - 26 q^{49} - 8 q^{51} - 4 q^{54} + 8 q^{56} + 32 q^{59} - 18 q^{64} - 28 q^{66} - 48 q^{71} - 32 q^{74} - 4 q^{76} + 40 q^{79} - 30 q^{81} + 16 q^{84} + 8 q^{86} + 64 q^{89} + 12 q^{91} - 40 q^{94} + 4 q^{96} + 104 q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
650.2.b.a $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+3iq^{3}-q^{4}-3q^{6}+iq^{7}+\cdots\)
650.2.b.b $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+2iq^{3}-q^{4}-2q^{6}+5iq^{7}+\cdots\)
650.2.b.c $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-4iq^{7}+\cdots\)
650.2.b.d $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+iq^{7}-iq^{8}+\cdots\)
650.2.b.e $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+3q^{9}-iq^{13}+\cdots\)
650.2.b.f $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+4iq^{7}+\cdots\)
650.2.b.g $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-4iq^{7}+\cdots\)
650.2.b.h $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+iq^{7}+\cdots\)
650.2.b.i $2$ $5.190$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-3iq^{3}-q^{4}+3q^{6}-iq^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(650, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)