Properties

Label 2028.2.w
Level $2028$
Weight $2$
Character orbit 2028.w
Rep. character $\chi_{2028}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $616$
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.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 52 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(728\)

Dimensions

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

Total New Old
Modular forms 1568 616 952
Cusp forms 1344 616 728
Eisenstein series 224 0 224

Trace form

\( 616 q + 4 q^{5} + 308 q^{9} + O(q^{10}) \) \( 616 q + 4 q^{5} + 308 q^{9} + 32 q^{14} + 16 q^{16} + 52 q^{20} - 8 q^{21} + 4 q^{22} - 12 q^{24} + 28 q^{28} + 80 q^{32} + 24 q^{34} + 12 q^{37} - 72 q^{40} + 56 q^{41} - 12 q^{42} - 56 q^{44} + 8 q^{45} - 36 q^{46} - 16 q^{48} + 72 q^{49} - 52 q^{50} + 56 q^{53} - 108 q^{56} + 48 q^{57} - 56 q^{58} - 16 q^{60} + 36 q^{61} - 60 q^{62} - 32 q^{66} + 48 q^{68} + 16 q^{70} + 76 q^{73} - 48 q^{74} + 12 q^{76} + 4 q^{80} - 308 q^{81} + 60 q^{82} - 4 q^{85} + 12 q^{88} - 100 q^{89} - 168 q^{92} + 8 q^{93} - 36 q^{94} + 40 q^{96} - 36 q^{97} - 148 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2028, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(676, [\chi])\)\(^{\oplus 2}\)