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Properties

Label 1872.4.dh
Level $1872$
Weight $4$
Character orbit 1872.dh
Rep. character $\chi_{1872}(673,\cdot)$
Character field $\Q(\zeta_{6})$
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.dh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 500 q + q^{3} + 3 q^{7} - q^{9} + O(q^{10}) \) \( 500 q + q^{3} + 3 q^{7} - q^{9} - q^{13} + 3 q^{15} - 2 q^{17} + 6 q^{19} - 81 q^{21} + 275 q^{23} + 6048 q^{25} + 70 q^{27} - 2 q^{29} + 270 q^{31} - 3 q^{33} + 967 q^{35} - 6 q^{37} - 151 q^{39} - 3 q^{41} - 127 q^{43} - 378 q^{45} + 11663 q^{49} + 106 q^{51} - 8 q^{53} + 127 q^{55} - 1272 q^{57} + q^{61} + 3 q^{63} - 715 q^{65} + 3 q^{67} + 573 q^{69} - 2622 q^{71} + 278 q^{75} + 1012 q^{77} + 2 q^{79} - 153 q^{81} + 1123 q^{87} - 6 q^{89} + 651 q^{91} - 171 q^{93} - 6328 q^{95} - 3 q^{97} - 7839 q^{99} + O(q^{100}) \)

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

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