↑

Properties

Label 1200.3.cb
Level $1200$
Weight $3$
Character orbit 1200.cb
Rep. character $\chi_{1200}(161,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1200 = 2^{4} \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1200.cb (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1968 488 1480
Cusp forms 1872 472 1400
Eisenstein series 96 16 80

Trace form

\( 472 q + 3 q^{3} + 16 q^{7} - 3 q^{9} + O(q^{10}) \) \( 472 q + 3 q^{3} + 16 q^{7} - 3 q^{9} - 6 q^{13} + 37 q^{15} + 6 q^{19} - 30 q^{21} - 16 q^{25} - 93 q^{27} + 6 q^{31} - 21 q^{33} + 42 q^{37} - 15 q^{39} + 80 q^{43} - 29 q^{45} + 3032 q^{49} + 26 q^{51} - 54 q^{55} + 42 q^{57} + 154 q^{61} + 294 q^{63} + 198 q^{67} - 21 q^{69} - 118 q^{73} - 109 q^{75} + 6 q^{79} + 237 q^{81} + 374 q^{85} + 245 q^{87} + 300 q^{91} + 10 q^{93} - 30 q^{97} + 170 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1200, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(600, [\chi])\)\(^{\oplus 2}\)