Properties

Label 1200.4.bs
Level $1200$
Weight $4$
Character orbit 1200.bs
Rep. character $\chi_{1200}(289,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $360$
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.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 2928 360 2568
Cusp forms 2832 360 2472
Eisenstein series 96 0 96

Trace form

\( 360 q + 2 q^{5} + 810 q^{9} + O(q^{10}) \) \( 360 q + 2 q^{5} + 810 q^{9} + 228 q^{19} + 420 q^{23} + 62 q^{25} + 284 q^{29} + 372 q^{31} + 120 q^{35} - 330 q^{37} - 312 q^{39} + 236 q^{41} - 18 q^{45} - 17232 q^{49} + 2448 q^{51} + 1430 q^{53} + 1464 q^{55} - 156 q^{61} + 2178 q^{65} + 4620 q^{67} - 552 q^{75} - 1580 q^{79} - 7290 q^{81} + 10380 q^{83} - 718 q^{85} + 3420 q^{87} + 330 q^{89} - 2184 q^{91} - 8132 q^{95} - 1860 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1200, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(100, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(200, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(400, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)