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Properties

Label 1872.4.fv
Level $1872$
Weight $4$
Character orbit 1872.fv
Rep. character $\chi_{1872}(401,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1000$
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.fv (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 4080 1016 3064
Cusp forms 3984 1000 2984
Eisenstein series 96 16 80

Trace form

\( 1000 q + 2 q^{3} - 6 q^{5} + 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 1000 q + 2 q^{3} - 6 q^{5} + 2 q^{7} - 2 q^{9} + 6 q^{11} - 2 q^{13} - 104 q^{15} + 8 q^{19} + 50 q^{21} + 12 q^{23} + 8 q^{27} - 6 q^{29} - 178 q^{31} - 58 q^{33} - 8 q^{37} + 664 q^{39} - 6 q^{41} - 254 q^{45} + 6 q^{47} + 4 q^{55} + 898 q^{57} - 3054 q^{59} - 4 q^{61} + 1376 q^{63} - 6 q^{65} + 2 q^{67} - 6 q^{69} + 5256 q^{71} - 8 q^{73} + 6 q^{75} - 1968 q^{77} + 4 q^{79} - 2 q^{81} + 6 q^{83} + 498 q^{85} - 1918 q^{87} - 1972 q^{91} + 2136 q^{93} + 6 q^{95} - 2 q^{97} - 9336 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1872, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(234, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(468, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 2}\)