Properties

Label 1200.4.bo
Level $1200$
Weight $4$
Character orbit 1200.bo
Rep. character $\chi_{1200}(241,\cdot)$
Character field $\Q(\zeta_{5})$
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.bo (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
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

\( 360 q - 2 q^{5} - 810 q^{9} + O(q^{10}) \) \( 360 q - 2 q^{5} - 810 q^{9} + 92 q^{13} + 52 q^{17} + 228 q^{19} - 252 q^{23} - 106 q^{25} + 284 q^{29} - 372 q^{31} + 24 q^{33} - 576 q^{35} + 198 q^{37} - 312 q^{39} - 236 q^{41} - 432 q^{43} - 18 q^{45} + 408 q^{47} + 18048 q^{49} - 2448 q^{51} - 858 q^{53} - 528 q^{55} + 156 q^{61} - 2702 q^{65} - 2700 q^{67} + 1724 q^{73} + 552 q^{75} - 1580 q^{79} - 7290 q^{81} + 3548 q^{83} - 1058 q^{85} + 2052 q^{87} + 330 q^{89} + 2184 q^{91} + 3648 q^{93} - 3172 q^{95} - 2024 q^{97} + O(q^{100}) \)

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

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