Properties

Label 200.2.c
Level $200$
Weight $2$
Character orbit 200.c
Rep. character $\chi_{200}(49,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $2$
Sturm bound $60$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 200.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 42 4 38
Cusp forms 18 4 14
Eisenstein series 24 0 24

Trace form

\( 4q - 6q^{9} + O(q^{10}) \) \( 4q - 6q^{9} + 10q^{11} - 10q^{19} - 12q^{21} + 20q^{29} + 4q^{31} + 24q^{39} - 18q^{41} - 12q^{49} - 30q^{51} - 8q^{59} + 16q^{61} - 12q^{69} - 24q^{71} - 12q^{79} + 36q^{81} + 30q^{89} + 32q^{91} + 12q^{99} + O(q^{100}) \)

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.c.a \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots\)
200.2.c.b \(2\) \(1.597\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)