Properties

Label 1200.2.bc
Level $1200$
Weight $2$
Character orbit 1200.bc
Rep. character $\chi_{1200}(43,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $144$
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.bc (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 504 144 360
Cusp forms 456 144 312
Eisenstein series 48 0 48

Trace form

\( 144 q - 8 q^{4} - 12 q^{8} - 144 q^{9} + O(q^{10}) \) \( 144 q - 8 q^{4} - 12 q^{8} - 144 q^{9} + 8 q^{12} - 8 q^{16} + 16 q^{19} - 12 q^{22} - 28 q^{28} + 20 q^{32} - 40 q^{34} + 8 q^{36} + 40 q^{38} + 20 q^{42} - 32 q^{43} - 24 q^{44} + 8 q^{46} - 48 q^{47} + 16 q^{48} + 16 q^{51} - 48 q^{52} - 24 q^{56} - 36 q^{58} - 64 q^{59} + 32 q^{61} - 56 q^{62} - 8 q^{64} + 48 q^{66} + 48 q^{67} + 16 q^{68} + 32 q^{69} + 128 q^{71} + 12 q^{72} + 16 q^{73} + 64 q^{74} - 56 q^{76} - 24 q^{78} + 144 q^{81} - 40 q^{82} - 48 q^{84} - 96 q^{86} - 76 q^{88} + 64 q^{91} + 24 q^{92} + 56 q^{94} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)