Properties

Label 200.2.k
Level $200$
Weight $2$
Character orbit 200.k
Rep. character $\chi_{200}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $32$
Newform subspaces $8$
Sturm bound $60$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 40 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 8 \)
Sturm bound: \(60\)
Trace bound: \(3\)
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 72 40 32
Cusp forms 48 32 16
Eisenstein series 24 8 16

Trace form

\( 32 q + 2 q^{2} + 4 q^{3} + 4 q^{6} - 4 q^{8} + O(q^{10}) \) \( 32 q + 2 q^{2} + 4 q^{3} + 4 q^{6} - 4 q^{8} - 8 q^{11} - 12 q^{12} - 28 q^{16} + 8 q^{17} - 10 q^{18} - 12 q^{22} - 52 q^{26} - 8 q^{27} + 20 q^{28} + 32 q^{32} + 16 q^{33} + 76 q^{36} + 4 q^{38} - 8 q^{41} + 20 q^{42} - 28 q^{43} + 8 q^{46} - 16 q^{48} - 40 q^{51} - 20 q^{52} - 32 q^{56} - 8 q^{57} - 20 q^{58} - 40 q^{62} - 100 q^{66} + 28 q^{67} + 4 q^{68} + 20 q^{72} - 16 q^{73} + 52 q^{76} + 40 q^{78} - 40 q^{81} + 28 q^{82} + 44 q^{83} + 96 q^{86} - 16 q^{88} + 56 q^{91} - 20 q^{92} + 44 q^{96} - 16 q^{97} + 6 q^{98} + O(q^{100}) \)

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.k.a 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(-2\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
200.2.k.b 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(-2\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots\)
200.2.k.c 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(2\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
200.2.k.d 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(2\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots\)
200.2.k.e 200.k 40.k $4$ $1.597$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(-4\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
200.2.k.f 200.k 40.k $4$ $1.597$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(4\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots\)
200.2.k.g 200.k 40.k $8$ $1.597$ 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
200.2.k.h 200.k 40.k $8$ $1.597$ \(\Q(\zeta_{20})\) None \(2\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots\)

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

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