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Properties

Label 1200.4.bb
Level $1200$
Weight $4$
Character orbit 1200.bb
Rep. character $\chi_{1200}(893,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $856$
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.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 240 \)
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 872 592
Cusp forms 1416 856 560
Eisenstein series 48 16 32

Trace form

\( 856 q - 24 q^{4} - 4 q^{6} + O(q^{10}) \) \( 856 q - 24 q^{4} - 4 q^{6} - 52 q^{12} + 256 q^{16} + 224 q^{18} - 48 q^{19} - 4 q^{21} + 252 q^{22} - 108 q^{24} - 172 q^{28} - 16 q^{31} + 4 q^{33} + 1848 q^{34} - 260 q^{36} + 216 q^{39} - 220 q^{42} - 856 q^{43} + 160 q^{46} + 2192 q^{48} - 4 q^{51} + 744 q^{52} + 2112 q^{54} - 108 q^{57} + 332 q^{58} - 1832 q^{61} + 1376 q^{63} + 3192 q^{64} - 3300 q^{66} + 8 q^{67} - 108 q^{69} - 2272 q^{72} + 5200 q^{76} + 3652 q^{78} - 8 q^{81} - 1632 q^{82} + 6084 q^{84} + 108 q^{87} + 3620 q^{88} - 8 q^{91} - 840 q^{94} - 2796 q^{96} + 8 q^{97} - 5312 q^{99} + O(q^{100}) \)

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

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