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Properties

Label 1200.4.y
Level $1200$
Weight $4$
Character orbit 1200.y
Rep. character $\chi_{1200}(643,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $432$
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.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 80 \)
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 432 1032
Cusp forms 1416 432 984
Eisenstein series 48 0 48

Trace form

\( 432 q - 24 q^{4} + 84 q^{8} + 3888 q^{9} + O(q^{10}) \) \( 432 q - 24 q^{4} + 84 q^{8} + 3888 q^{9} - 24 q^{12} - 264 q^{16} + 48 q^{19} - 44 q^{22} + 204 q^{28} + 340 q^{32} + 1240 q^{34} - 216 q^{36} - 2032 q^{38} - 660 q^{42} - 1032 q^{44} + 24 q^{46} + 816 q^{47} + 528 q^{48} + 1488 q^{51} + 2424 q^{52} + 168 q^{56} + 284 q^{58} - 2752 q^{59} - 1824 q^{61} + 2608 q^{62} + 456 q^{64} - 2736 q^{66} + 1464 q^{68} + 1056 q^{69} - 896 q^{71} + 756 q^{72} + 592 q^{73} + 4672 q^{74} + 5032 q^{76} - 72 q^{78} + 34992 q^{81} + 5920 q^{82} - 5360 q^{83} - 144 q^{84} - 4128 q^{86} + 1796 q^{88} + 3392 q^{91} - 4992 q^{92} - 3432 q^{94} + 1264 q^{98} + O(q^{100}) \)

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

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