↑

Properties

Label 1008.4.t
Level $1008$
Weight $4$
Character orbit 1008.t
Rep. character $\chi_{1008}(193,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $284$
Sturm bound $768$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.t (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1176 292 884
Cusp forms 1128 284 844
Eisenstein series 48 8 40

Trace form

\( 284 q + q^{3} - 2 q^{5} + q^{7} - q^{9} + O(q^{10}) \) \( 284 q + q^{3} - 2 q^{5} + q^{7} - q^{9} + 2 q^{11} - 2 q^{13} + 31 q^{15} - 2 q^{17} + 2 q^{19} - 192 q^{21} + 2 q^{23} + 6698 q^{25} + 4 q^{27} - 30 q^{29} + 89 q^{31} - 109 q^{33} + 129 q^{35} - 2 q^{37} - 329 q^{39} - 2 q^{41} - 124 q^{43} - 281 q^{45} + 939 q^{47} - q^{49} + 803 q^{51} - 2 q^{53} + 258 q^{55} + 474 q^{57} - 2125 q^{59} + q^{61} - 1167 q^{63} - 481 q^{65} - q^{67} - 7 q^{69} + 1760 q^{71} - 2 q^{73} - 162 q^{75} - 1701 q^{77} - q^{79} + 155 q^{81} - 3596 q^{83} + 123 q^{85} + 1306 q^{87} - 214 q^{89} + 308 q^{91} - 59 q^{93} + 1131 q^{95} - 2 q^{97} + 1357 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)