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Properties

Label 1200.4.bk
Level $1200$
Weight $4$
Character orbit 1200.bk
Rep. character $\chi_{1200}(251,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $900$
Sturm bound $960$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1200.bk (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1200, [\chi])\).

Total New Old
Modular forms 1464 924 540
Cusp forms 1416 900 516
Eisenstein series 48 24 24

Trace form

\( 900 q + 2 q^{3} + 4 q^{4} + 24 q^{6} + 8 q^{7} + O(q^{10}) \) \( 900 q + 2 q^{3} + 4 q^{4} + 24 q^{6} + 8 q^{7} - 76 q^{12} + 4 q^{13} - 384 q^{16} + 88 q^{18} - 20 q^{19} + 48 q^{21} - 464 q^{22} + 620 q^{24} - 130 q^{27} + 224 q^{28} + 4 q^{33} - 392 q^{34} + 88 q^{36} + 4 q^{37} + 604 q^{39} + 1564 q^{42} + 436 q^{43} + 760 q^{46} - 1240 q^{48} + 40580 q^{49} - 760 q^{51} + 2200 q^{52} - 1372 q^{54} + 1600 q^{58} + 900 q^{61} + 976 q^{64} - 1540 q^{66} - 1628 q^{67} + 164 q^{69} - 272 q^{72} - 888 q^{76} + 892 q^{78} - 12 q^{81} + 4320 q^{82} + 3092 q^{84} - 1284 q^{87} - 872 q^{88} + 3160 q^{91} - 2188 q^{93} + 8536 q^{94} - 1556 q^{96} + 8 q^{97} - 1196 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)