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Properties

Label 2028.2.bg
Level $2028$
Weight $2$
Character orbit 2028.bg
Rep. character $\chi_{2028}(61,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $696$
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.bg (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{39})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 8880 696 8184
Cusp forms 8592 696 7896
Eisenstein series 288 0 288

Trace form

\( 696 q - q^{3} - 4 q^{5} + q^{7} + 29 q^{9} + O(q^{10}) \) \( 696 q - q^{3} - 4 q^{5} + q^{7} + 29 q^{9} + 2 q^{11} + 8 q^{13} - 2 q^{15} + 4 q^{19} + 2 q^{21} + 2 q^{23} - 46 q^{25} + 2 q^{27} + 6 q^{29} + 54 q^{31} - 2 q^{33} - 2 q^{35} + 10 q^{37} + 2 q^{39} - 4 q^{41} - 3 q^{43} + 2 q^{45} + 20 q^{47} + 74 q^{49} + 114 q^{53} + 26 q^{55} + 8 q^{57} - 2 q^{59} - 5 q^{61} + q^{63} - 10 q^{65} + 149 q^{67} - 10 q^{69} + 166 q^{71} + 14 q^{73} + q^{75} - 20 q^{77} - 26 q^{79} + 29 q^{81} - 24 q^{83} + 122 q^{85} + 50 q^{87} - 16 q^{89} + 111 q^{91} - 103 q^{93} + 220 q^{95} + 169 q^{97} - 4 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(169, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(338, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)