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Properties

Label 2028.2.bf
Level $2028$
Weight $2$
Character orbit 2028.bf
Rep. character $\chi_{2028}(25,\cdot)$
Character field $\Q(\zeta_{26})$
Dimension $384$
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.bf (of order \(26\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 169 \)
Character field: \(\Q(\zeta_{26})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 4440 384 4056
Cusp forms 4296 384 3912
Eisenstein series 144 0 144

Trace form

\( 384 q - 32 q^{9} + O(q^{10}) \) \( 384 q - 32 q^{9} - 4 q^{13} - 4 q^{17} + 12 q^{23} + 36 q^{25} + 8 q^{29} + 52 q^{31} + 20 q^{35} - 8 q^{39} - 4 q^{43} + 84 q^{49} + 12 q^{51} + 80 q^{53} - 74 q^{55} - 24 q^{61} + 16 q^{65} - 52 q^{67} + 12 q^{69} - 78 q^{71} - 16 q^{75} - 40 q^{77} + 20 q^{79} - 32 q^{81} - 104 q^{85} + 32 q^{87} + 88 q^{91} - 78 q^{93} - 148 q^{95} - 156 q^{97} + O(q^{100}) \)

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

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