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Properties

Label 1045.2.bm
Level $1045$
Weight $2$
Character orbit 1045.bm
Rep. character $\chi_{1045}(21,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1045.bm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1045, [\chi])\).

Total New Old
Modular forms 744 480 264
Cusp forms 696 480 216
Eisenstein series 48 0 48

Trace form

\( 480 q - 12 q^{3} - 36 q^{9} + O(q^{10}) \) \( 480 q - 12 q^{3} - 36 q^{9} - 24 q^{14} + 24 q^{22} + 60 q^{26} + 36 q^{27} - 36 q^{31} - 144 q^{34} + 36 q^{36} + 24 q^{38} + 36 q^{42} - 12 q^{44} + 96 q^{47} - 204 q^{48} + 264 q^{49} + 72 q^{53} + 96 q^{58} - 108 q^{59} - 240 q^{64} - 126 q^{66} + 36 q^{67} + 108 q^{69} - 144 q^{70} + 12 q^{71} + 36 q^{77} + 300 q^{78} - 348 q^{81} + 36 q^{82} - 12 q^{86} - 144 q^{88} + 72 q^{89} - 24 q^{91} - 48 q^{93} - 60 q^{97} - 54 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)