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Properties

Label 2672.2.m
Level $2672$
Weight $2$
Character orbit 2672.m
Rep. character $\chi_{2672}(33,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $6806$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2672 = 2^{4} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2672.m (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2672, [\chi])\).

Total New Old
Modular forms 28044 6970 21074
Cusp forms 27060 6806 20254
Eisenstein series 984 164 820

Trace form

\( 6806 q + 81 q^{3} - 81 q^{5} + 81 q^{7} - 162 q^{9} + O(q^{10}) \) \( 6806 q + 81 q^{3} - 81 q^{5} + 81 q^{7} - 162 q^{9} + 81 q^{11} - 81 q^{13} + 71 q^{15} - 81 q^{17} + 73 q^{19} - 83 q^{21} + 75 q^{23} - 160 q^{25} + 63 q^{27} - 89 q^{29} + 73 q^{31} - 75 q^{33} + 83 q^{35} - 81 q^{37} + 79 q^{39} - 89 q^{41} + 71 q^{43} - 73 q^{45} + 93 q^{47} - 166 q^{49} + 103 q^{51} - 89 q^{53} + 71 q^{55} - 75 q^{57} + 83 q^{59} - 73 q^{61} + 97 q^{63} - 79 q^{65} + 111 q^{67} - 83 q^{69} + 87 q^{71} - 81 q^{73} + 57 q^{75} - 91 q^{77} + 75 q^{79} - 142 q^{81} + 91 q^{83} - 55 q^{85} + 95 q^{87} - 81 q^{89} + 63 q^{91} - 67 q^{93} + 95 q^{95} - 81 q^{97} + 85 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2672, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2672, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(334, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1336, [\chi])\)\(^{\oplus 2}\)