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Properties

Label 1872.2.r
Level $1872$
Weight $2$
Character orbit 1872.r
Rep. character $\chi_{1872}(1537,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $164$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1872.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 117 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1872, [\chi])\).

Total New Old
Modular forms 696 172 524
Cusp forms 648 164 484
Eisenstein series 48 8 40

Trace form

\( 164 q + q^{3} - 2 q^{5} - q^{7} - q^{9} + O(q^{10}) \) \( 164 q + q^{3} - 2 q^{5} - q^{7} - q^{9} + 2 q^{11} - q^{13} - 5 q^{15} - 2 q^{17} + 2 q^{19} - 7 q^{21} - 13 q^{23} - 76 q^{25} + 10 q^{27} - 2 q^{29} - 4 q^{31} - 13 q^{33} + 21 q^{35} - 2 q^{37} + 5 q^{39} + q^{41} - 7 q^{43} - 6 q^{45} + 2 q^{47} - 69 q^{49} - 14 q^{51} - 8 q^{53} - 3 q^{55} + 10 q^{57} - 22 q^{59} + q^{61} - 13 q^{63} - 7 q^{65} - q^{67} + 13 q^{69} + 14 q^{71} - 8 q^{73} - 6 q^{75} - 24 q^{77} + 2 q^{79} + 7 q^{81} + 2 q^{83} - 12 q^{85} + 19 q^{87} - 2 q^{89} + 17 q^{91} - 35 q^{93} + 76 q^{95} + q^{97} - 31 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1872, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1872, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1872, [\chi]) \cong \)