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Properties

Label 2700.2.by
Level $2700$
Weight $2$
Character orbit 2700.by
Rep. character $\chi_{2700}(289,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $240$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2700.by (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 225 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2700, [\chi])\).

Total New Old
Modular forms 4464 240 4224
Cusp forms 4176 240 3936
Eisenstein series 288 0 288

Trace form

\( 240 q - 4 q^{5} + O(q^{10}) \) \( 240 q - 4 q^{5} + 4 q^{11} - 12 q^{25} - 12 q^{29} - 6 q^{31} - 34 q^{35} + 16 q^{41} - 25 q^{47} + 120 q^{49} + 6 q^{55} - 9 q^{59} - 35 q^{65} + 15 q^{67} + 38 q^{71} + 40 q^{77} + 12 q^{79} - 70 q^{83} + 12 q^{85} + 58 q^{89} + 36 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2700, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2700, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(900, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)