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Properties

Label 1872.4.s
Level $1872$
Weight $4$
Character orbit 1872.s
Rep. character $\chi_{1872}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $500$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1872.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1872, [\chi])\).

Total New Old
Modular forms 2040 508 1532
Cusp forms 1992 500 1492
Eisenstein series 48 8 40

Trace form

\( 500 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9} + O(q^{10}) \) \( 500 q + q^{3} - 2 q^{5} + 2 q^{7} - q^{9} - q^{11} - q^{13} + 28 q^{15} - 2 q^{17} + 2 q^{19} - 31 q^{21} - 550 q^{23} - 6052 q^{25} - 62 q^{27} + q^{29} + 92 q^{31} + 53 q^{33} - 963 q^{35} - 2 q^{37} - 370 q^{39} - 2 q^{41} + 254 q^{43} + 249 q^{45} + 2 q^{47} + 23322 q^{49} - 206 q^{51} - 8 q^{53} - 123 q^{55} - 374 q^{57} + 1019 q^{59} - 2 q^{61} + 1373 q^{63} + 17 q^{65} + 2 q^{67} - 629 q^{69} + 878 q^{71} - 8 q^{73} + 72 q^{75} - 360 q^{77} + 2 q^{79} + 151 q^{81} + 2 q^{83} + 126 q^{85} + 961 q^{87} - 2 q^{89} + 1337 q^{91} - 2276 q^{93} + 2914 q^{95} - 2 q^{97} + 1505 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \)