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Properties

Label 2805.2.dw
Level $2805$
Weight $2$
Character orbit 2805.dw
Rep. character $\chi_{2805}(52,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1536$
Sturm bound $864$

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Defining parameters

Level: \( N \) \(=\) \( 2805 = 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2805.dw (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(864\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2805, [\chi])\).

Total New Old
Modular forms 3520 1536 1984
Cusp forms 3392 1536 1856
Eisenstein series 128 0 128

Trace form

\( 1536 q + O(q^{10}) \) \( 1536 q - 16 q^{11} + 32 q^{12} + 24 q^{15} + 384 q^{16} + 120 q^{20} + 48 q^{22} - 32 q^{26} + 120 q^{28} + 80 q^{30} + 28 q^{33} + 384 q^{36} - 48 q^{37} + 240 q^{41} - 24 q^{42} + 480 q^{46} - 136 q^{47} - 96 q^{48} - 160 q^{50} - 72 q^{53} - 80 q^{55} + 288 q^{56} + 24 q^{58} - 48 q^{60} - 160 q^{62} - 24 q^{66} - 32 q^{67} + 120 q^{70} + 120 q^{73} - 72 q^{77} + 192 q^{78} + 384 q^{81} - 16 q^{82} + 400 q^{83} + 160 q^{86} + 152 q^{88} - 16 q^{91} - 120 q^{92} - 160 q^{95} - 32 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2805, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)