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Properties

Label 1200.3.be
Level $1200$
Weight $3$
Character orbit 1200.be
Rep. character $\chi_{1200}(157,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.be (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1200, [\chi])\).

Total New Old
Modular forms 984 288 696
Cusp forms 936 288 648
Eisenstein series 48 0 48

Trace form

\( 288 q - 8 q^{4} - 12 q^{8} + 864 q^{9} + O(q^{10}) \) \( 288 q - 8 q^{4} - 12 q^{8} + 864 q^{9} - 24 q^{12} + 56 q^{16} - 64 q^{19} - 4 q^{22} - 124 q^{28} - 140 q^{32} + 296 q^{34} - 24 q^{36} + 104 q^{38} + 60 q^{42} - 24 q^{44} + 56 q^{46} + 144 q^{48} - 192 q^{51} + 352 q^{52} + 168 q^{56} + 452 q^{58} - 256 q^{59} - 64 q^{61} + 8 q^{62} + 88 q^{64} + 144 q^{66} + 352 q^{68} + 192 q^{69} - 36 q^{72} - 96 q^{73} - 64 q^{74} + 296 q^{76} + 216 q^{78} + 2592 q^{81} - 328 q^{82} + 320 q^{83} - 432 q^{84} + 96 q^{86} - 140 q^{88} + 768 q^{91} - 408 q^{92} + 680 q^{94} - 768 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1200, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 2}\)