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Properties

Label 2028.2.y
Level $2028$
Weight $2$
Character orbit 2028.y
Rep. character $\chi_{2028}(157,\cdot)$
Character field $\Q(\zeta_{13})$
Dimension $360$
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.y (of order \(13\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{13})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 4440 360 4080
Cusp forms 4296 360 3936
Eisenstein series 144 0 144

Trace form

\( 360 q + 4 q^{5} - 30 q^{9} + O(q^{10}) \) \( 360 q + 4 q^{5} - 30 q^{9} + 4 q^{11} - 2 q^{13} - 4 q^{15} - 4 q^{21} + 4 q^{23} - 30 q^{25} + 12 q^{29} - 44 q^{31} - 4 q^{33} - 4 q^{35} - 12 q^{37} + 4 q^{41} + 4 q^{43} + 4 q^{45} + 4 q^{47} - 74 q^{49} + 12 q^{51} - 126 q^{53} - 38 q^{55} - 4 q^{57} - 4 q^{59} + 12 q^{61} + 4 q^{65} - 148 q^{67} + 4 q^{69} + 50 q^{71} - 4 q^{73} + 16 q^{75} - 16 q^{77} + 12 q^{79} - 30 q^{81} - 12 q^{83} - 122 q^{85} - 56 q^{87} + 4 q^{89} - 104 q^{91} + 66 q^{93} + 92 q^{95} - 144 q^{97} + 4 q^{99} + O(q^{100}) \)

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

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