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Properties

Label 2805.2.bb
Level $2805$
Weight $2$
Character orbit 2805.bb
Rep. character $\chi_{2805}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $384$
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.bb (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(864\)

Dimensions

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

Total New Old
Modular forms 880 384 496
Cusp forms 848 384 464
Eisenstein series 32 0 32

Trace form

\( 384 q + O(q^{10}) \) \( 384 q + 16 q^{11} - 32 q^{12} + 16 q^{15} - 384 q^{16} + 80 q^{20} - 48 q^{22} + 32 q^{26} - 28 q^{33} - 384 q^{36} + 48 q^{37} - 16 q^{42} + 16 q^{47} - 64 q^{48} - 48 q^{53} + 80 q^{55} - 288 q^{56} - 64 q^{58} - 32 q^{60} + 24 q^{66} + 32 q^{67} + 80 q^{70} + 72 q^{77} + 48 q^{78} - 384 q^{81} + 96 q^{82} - 160 q^{86} - 72 q^{88} - 64 q^{91} - 80 q^{92} - 208 q^{97} + O(q^{100}) \)

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

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