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Properties

Label 2028.4.bu
Level $2028$
Weight $4$
Character orbit 2028.bu
Rep. character $\chi_{2028}(41,\cdot)$
Character field $\Q(\zeta_{156})$
Dimension $8736$
Sturm bound $1456$

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Defining parameters

Level: \( N \) \(=\) \( 2028 = 2^{2} \cdot 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2028.bu (of order \(156\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 507 \)
Character field: \(\Q(\zeta_{156})\)
Sturm bound: \(1456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(2028, [\chi])\).

Total New Old
Modular forms 52704 8736 43968
Cusp forms 52128 8736 43392
Eisenstein series 576 0 576

Trace form

\( 8736 q - 64 q^{7} + O(q^{10}) \) \( 8736 q - 64 q^{7} + 120 q^{13} + 48 q^{15} - 448 q^{19} - 192 q^{21} - 312 q^{27} + 184 q^{31} + 516 q^{33} - 380 q^{37} + 5432 q^{39} + 336 q^{43} - 5132 q^{45} + 828 q^{49} - 4368 q^{55} + 612 q^{57} + 312 q^{61} - 8740 q^{63} + 11600 q^{67} + 2028 q^{69} + 2564 q^{73} - 9340 q^{75} + 1872 q^{79} + 208 q^{81} + 4824 q^{85} - 208 q^{87} - 592 q^{91} - 11888 q^{93} + 3892 q^{97} + 2592 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(2028, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(2028, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(2028, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(507, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(1014, [\chi])\)\(^{\oplus 2}\)