Properties

Label 200.2.v
Level $200$
Weight $2$
Character orbit 200.v
Rep. character $\chi_{200}(3,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $224$
Newform subspaces $3$
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.v (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 200 \)
Character field: \(\Q(\zeta_{20})\)
Newform subspaces: \( 3 \)
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 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

Trace form

\( 224q - 8q^{2} - 16q^{3} - 10q^{4} - 6q^{6} - 14q^{8} - 20q^{9} + O(q^{10}) \) \( 224q - 8q^{2} - 16q^{3} - 10q^{4} - 6q^{6} - 14q^{8} - 20q^{9} - 12q^{11} - 22q^{12} - 10q^{14} - 6q^{16} - 12q^{17} - 20q^{18} - 20q^{19} - 10q^{20} - 22q^{22} - 20q^{25} - 16q^{26} - 28q^{27} + 10q^{28} - 30q^{30} + 22q^{32} - 4q^{33} - 10q^{34} - 40q^{35} - 22q^{36} - 36q^{38} + 60q^{40} - 12q^{41} - 90q^{42} - 48q^{43} + 60q^{44} - 6q^{46} + 104q^{48} - 90q^{50} - 32q^{51} + 60q^{52} - 140q^{54} - 6q^{56} - 28q^{57} - 100q^{58} - 20q^{59} + 70q^{60} - 100q^{62} + 20q^{64} - 20q^{65} + 18q^{66} + 8q^{67} - 6q^{68} - 30q^{70} + 40q^{72} - 36q^{73} + 40q^{75} - 32q^{76} - 10q^{80} + 12q^{81} + 58q^{82} + 24q^{83} + 70q^{84} - 6q^{86} + 94q^{88} - 120q^{89} + 150q^{90} - 12q^{91} + 70q^{92} + 150q^{94} - 26q^{96} + 44q^{97} + 156q^{98} + O(q^{100}) \)

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.v.a \(8\) \(1.597\) \(\Q(\zeta_{20})\) None \(-8\) \(0\) \(10\) \(4\) \(q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.b \(8\) \(1.597\) \(\Q(\zeta_{20})\) None \(-2\) \(0\) \(-10\) \(-4\) \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.c \(208\) \(1.597\) None \(2\) \(-16\) \(0\) \(0\)