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Properties

Label 550.2.b
Level $550$
Weight $2$
Character orbit 550.b
Rep. character $\chi_{550}(199,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $6$
Sturm bound $180$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 550.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(180\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(550, [\chi])\).

Total New Old
Modular forms 102 14 88
Cusp forms 78 14 64
Eisenstein series 24 0 24

Trace form

\( 14 q - 14 q^{4} + 8 q^{6} - 14 q^{9} + O(q^{10}) \) \( 14 q - 14 q^{4} + 8 q^{6} - 14 q^{9} - 2 q^{11} + 14 q^{16} + 8 q^{19} - 16 q^{21} - 8 q^{24} - 24 q^{26} + 4 q^{29} - 4 q^{31} + 28 q^{34} + 14 q^{36} - 8 q^{39} + 44 q^{41} + 2 q^{44} + 24 q^{46} - 38 q^{49} - 32 q^{51} - 32 q^{54} - 32 q^{59} + 12 q^{61} - 14 q^{64} - 8 q^{66} + 48 q^{69} + 4 q^{71} + 12 q^{74} - 8 q^{76} + 24 q^{79} + 14 q^{81} + 16 q^{84} + 4 q^{86} + 24 q^{89} - 56 q^{91} + 8 q^{94} + 8 q^{96} + 26 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(550, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
550.2.b.a $2$ $4.392$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}+3iq^{7}+\cdots\)
550.2.b.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}+iq^{3}-q^{4}-q^{6}-5iq^{7}+\cdots\)
550.2.b.c $2$ $4.392$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-iq^{3}-q^{4}+q^{6}-iq^{7}-iq^{8}+\cdots\)
550.2.b.d $2$ $4.392$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}+4iq^{7}+\cdots\)
550.2.b.e $2$ $4.392$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-2iq^{3}-q^{4}+2q^{6}-iq^{8}+\cdots\)
550.2.b.f $4$ $4.392$ \(\Q(i, \sqrt{33})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(550, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(550, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)