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Properties

Label 2730.2.ey
Level $2730$
Weight $2$
Character orbit 2730.ey
Rep. character $\chi_{2730}(11,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $592$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2730 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2730.ey (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2730, [\chi])\).

Total New Old
Modular forms 2752 592 2160
Cusp forms 2624 592 2032
Eisenstein series 128 0 128

Trace form

\( 592 q - 24 q^{7} + O(q^{10}) \) \( 592 q - 24 q^{7} + 8 q^{15} + 296 q^{16} + 32 q^{18} - 40 q^{19} - 16 q^{21} - 32 q^{28} - 8 q^{31} + 16 q^{33} - 24 q^{36} + 72 q^{37} + 16 q^{39} - 24 q^{42} - 168 q^{43} + 32 q^{46} + 8 q^{49} - 8 q^{52} - 48 q^{54} - 16 q^{55} + 32 q^{58} + 8 q^{60} - 64 q^{61} + 8 q^{63} - 32 q^{66} + 160 q^{67} - 16 q^{72} + 272 q^{73} + 80 q^{76} - 32 q^{79} + 48 q^{81} + 16 q^{84} + 96 q^{85} + 32 q^{87} + 48 q^{91} + 80 q^{93} + 64 q^{94} + 8 q^{97} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2730, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2730, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2730, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(546, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1365, [\chi])\)\(^{\oplus 2}\)