↑

Properties

Label 900.4.i
Level $900$
Weight $4$
Character orbit 900.i
Rep. character $\chi_{900}(301,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $114$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 900.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(900, [\chi])\).

Total New Old
Modular forms 1116 114 1002
Cusp forms 1044 114 930
Eisenstein series 72 0 72

Trace form

\( 114 q + q^{3} - 6 q^{7} - 29 q^{9} + O(q^{10}) \) \( 114 q + q^{3} - 6 q^{7} - 29 q^{9} - q^{11} + 12 q^{13} - 126 q^{17} + 30 q^{19} - 80 q^{21} - 126 q^{23} - 56 q^{27} - 336 q^{29} + 12 q^{31} - 135 q^{33} - 240 q^{37} + 516 q^{39} - 427 q^{41} + 129 q^{43} - 246 q^{47} - 2475 q^{49} - 1763 q^{51} - 1224 q^{53} + 467 q^{57} - 413 q^{59} - 438 q^{61} + 80 q^{63} + 399 q^{67} - 1142 q^{69} - 1800 q^{71} + 750 q^{73} - 1032 q^{77} - 132 q^{79} + 919 q^{81} + 384 q^{83} - 1314 q^{87} + 524 q^{89} + 744 q^{91} + 3374 q^{93} + 453 q^{97} - 856 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(900, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(900, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(900, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 3}\)