Properties

Label 1200.2.bk
Level $1200$
Weight $2$
Character orbit 1200.bk
Rep. character $\chi_{1200}(251,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $292$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1200.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1200, [\chi])\).

Total New Old
Modular forms 504 316 188
Cusp forms 456 292 164
Eisenstein series 48 24 24

Trace form

\( 292 q + 2 q^{3} + 4 q^{4} - 12 q^{6} + 8 q^{7} + O(q^{10}) \) \( 292 q + 2 q^{3} + 4 q^{4} - 12 q^{6} + 8 q^{7} - 4 q^{12} + 4 q^{13} + 16 q^{18} + 12 q^{19} + 8 q^{22} - 4 q^{24} + 14 q^{27} + 32 q^{28} + 4 q^{33} + 40 q^{34} - 8 q^{36} + 4 q^{37} + 28 q^{39} + 4 q^{42} - 12 q^{43} - 8 q^{46} + 8 q^{48} + 228 q^{49} + 8 q^{51} + 8 q^{52} + 8 q^{54} + 72 q^{58} - 28 q^{61} + 16 q^{64} - 76 q^{66} + 36 q^{67} + 20 q^{69} + 16 q^{72} - 104 q^{76} - 20 q^{78} - 12 q^{81} + 48 q^{82} - 28 q^{84} + 60 q^{87} + 56 q^{88} - 8 q^{91} + 20 q^{93} - 88 q^{94} - 20 q^{96} + 8 q^{97} + 52 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)