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

\( 14 q - 14 q^{4} + 8 q^{6} - 14 q^{9} - 2 q^{11} + 14 q^{16} + 8 q^{19} - 16 q^{21} - 8 q^{24} - 24 q^{26} + 4 q^{29} - 4 q^{31} + 28 q^{34} + 14 q^{36} - 8 q^{39} + 44 q^{41} + 2 q^{44} + 24 q^{46} - 38 q^{49}+ \cdots + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
550.2.b.a 550.b 5.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None 110.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+i q^{3}-q^{4}-q^{6}+3 i q^{7}+\cdots\)
550.2.b.b 550.b 5.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None 110.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}+i q^{3}-q^{4}-q^{6}-5 i q^{7}+\cdots\)
550.2.b.c 550.b 5.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None 110.2.a.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-i q^{3}-q^{4}+q^{6}-i q^{7}+\cdots\)
550.2.b.d 550.b 5.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None 550.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}+4 i q^{7}+\cdots\)
550.2.b.e 550.b 5.b $2$ $4.392$ \(\Q(\sqrt{-1}) \) None 550.2.a.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+i q^{2}-2 i q^{3}-q^{4}+2 q^{6}-i q^{8}+\cdots\)
550.2.b.f 550.b 5.b $4$ $4.392$ \(\Q(i, \sqrt{33})\) None 110.2.a.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-q^{4}+\beta _{3}q^{6}+\cdots\)

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

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