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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
200.2.k.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(-2\) \(-4\) \(0\) \(0\) \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
200.2.k.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(-2\) \(0\) \(0\) \(-4\) \(q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots\)
200.2.k.c \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) \(2\) \(0\) \(0\) \(4\) \(q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
200.2.k.d \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) \(2\) \(4\) \(0\) \(0\) \(q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots\)
200.2.k.e \(4\) \(1.597\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(-4\) \(4\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
200.2.k.f \(4\) \(1.597\) \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) \(4\) \(-4\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots\)
200.2.k.g \(8\) \(1.597\) 8.0.3317760000.5 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
200.2.k.h \(8\) \(1.597\) \(\Q(\zeta_{20})\) None \(2\) \(4\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots\)

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

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