Properties

Label 200.14.j
Level $200$
Weight $14$
Character orbit 200.j
Rep. character $\chi_{200}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $0$
Newform subspaces $0$
Sturm bound $420$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 200 = 2^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 200.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 0 \)
Sturm bound: \(420\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(200, [\chi])\).

Total New Old
Modular forms 804 0 804
Cusp forms 756 0 756
Eisenstein series 48 0 48

Decomposition of \(S_{14}^{\mathrm{old}}(200, [\chi])\) into lower level spaces

\( S_{14}^{\mathrm{old}}(200, [\chi]) \simeq \) \(S_{14}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 2}\)