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Properties

Label 2700.2.bm
Level $2700$
Weight $2$
Character orbit 2700.bm
Rep. character $\chi_{2700}(49,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $324$
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.bm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 135 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 3348 324 3024
Cusp forms 3132 324 2808
Eisenstein series 216 0 216

Trace form

\( 324 q + 12 q^{9} + O(q^{10}) \) \( 324 q + 12 q^{9} - 12 q^{11} - 36 q^{21} - 12 q^{29} + 18 q^{31} - 54 q^{39} - 48 q^{41} - 36 q^{49} + 12 q^{51} - 42 q^{59} + 36 q^{61} - 24 q^{69} - 72 q^{79} + 12 q^{81} + 102 q^{89} + 84 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2700, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(540, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(675, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1350, [\chi])\)\(^{\oplus 2}\)