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Properties

Label 2028.2.bu
Level $2028$
Weight $2$
Character orbit 2028.bu
Rep. character $\chi_{2028}(41,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $2928$
Sturm bound $728$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2028.bu (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2028, [\chi])\).

Total New Old
Modular forms 17760 2928 14832
Cusp forms 17184 2928 14256
Eisenstein series 576 0 576

Trace form

\( 2928 q + 2 q^{7} + O(q^{10}) \) \( 2928 q + 2 q^{7} - 12 q^{15} - 10 q^{19} + 12 q^{21} + 12 q^{27} + 10 q^{31} + 30 q^{33} - 2 q^{37} + 104 q^{39} + 42 q^{43} + 160 q^{45} + 18 q^{49} + 112 q^{55} - 18 q^{57} + 8 q^{61} - 160 q^{63} - 176 q^{67} - 78 q^{69} - 10 q^{73} - 220 q^{75} - 64 q^{79} - 20 q^{81} - 96 q^{85} - 16 q^{87} - 22 q^{91} + 82 q^{93} - 38 q^{97} + 18 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)