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Properties

Label 2200.2.ec
Level $2200$
Weight $2$
Character orbit 2200.ec
Rep. character $\chi_{2200}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $216$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2200.ec (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2200, [\chi])\).

Total New Old
Modular forms 1536 216 1320
Cusp forms 1344 216 1128
Eisenstein series 192 0 192

Trace form

\( 216 q + 54 q^{9} + O(q^{10}) \) \( 216 q + 54 q^{9} - 4 q^{11} + 20 q^{19} - 32 q^{21} - 12 q^{29} - 28 q^{31} + 88 q^{39} - 20 q^{41} + 114 q^{49} - 84 q^{51} + 26 q^{59} + 12 q^{61} - 36 q^{69} + 64 q^{71} - 56 q^{79} - 86 q^{81} - 8 q^{89} - 12 q^{91} + 70 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2200, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2200, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2200, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(220, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(550, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1100, [\chi])\)\(^{\oplus 2}\)