Properties

Label 200.2.d
Level $200$
Weight $2$
Character orbit 200.d
Rep. character $\chi_{200}(101,\cdot)$
Character field $\Q$
Dimension $16$
Newform subspaces $6$
Sturm bound $60$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(60\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(200, [\chi])\).

Total New Old
Modular forms 36 22 14
Cusp forms 24 16 8
Eisenstein series 12 6 6

Trace form

\( 16 q + 2 q^{2} - 2 q^{4} - 10 q^{6} + 4 q^{7} + 8 q^{8} - 8 q^{9} + O(q^{10}) \) \( 16 q + 2 q^{2} - 2 q^{4} - 10 q^{6} + 4 q^{7} + 8 q^{8} - 8 q^{9} + 4 q^{12} - 14 q^{16} - 14 q^{18} - 4 q^{22} + 4 q^{23} + 14 q^{24} + 12 q^{26} - 12 q^{28} - 8 q^{31} - 8 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} + 20 q^{38} + 4 q^{42} + 6 q^{44} - 20 q^{47} + 24 q^{48} + 8 q^{49} + 26 q^{54} - 48 q^{56} - 8 q^{57} - 24 q^{58} - 16 q^{62} + 20 q^{63} - 14 q^{64} + 42 q^{66} - 24 q^{68} - 8 q^{72} - 16 q^{73} - 36 q^{74} + 30 q^{76} + 24 q^{78} + 40 q^{79} - 32 q^{81} + 8 q^{82} - 24 q^{84} - 12 q^{86} + 48 q^{87} + 16 q^{88} + 36 q^{92} - 48 q^{94} + 14 q^{96} + 16 q^{97} - 18 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(200, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.2.d.a 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots\)
200.2.d.b 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.c 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.d 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots\)
200.2.d.e 200.d 8.b $4$ $1.597$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.2.d.f 200.d 8.b $4$ $1.597$ \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)