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Properties

Label 1045.6.bm
Level $1045$
Weight $6$
Character orbit 1045.bm
Rep. character $\chi_{1045}(21,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $2400$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bm (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 3624 2400 1224
Cusp forms 3576 2400 1176
Eisenstein series 48 0 48

Trace form

\( 2400 q + 132 q^{3} + 396 q^{9} + O(q^{10}) \) \( 2400 q + 132 q^{3} + 396 q^{9} + 5280 q^{14} - 4224 q^{22} + 94644 q^{27} + 39276 q^{31} - 35100 q^{33} - 56616 q^{34} + 157464 q^{36} + 48096 q^{38} + 272244 q^{42} + 52110 q^{44} - 236256 q^{47} + 666204 q^{48} + 2928456 q^{49} + 157608 q^{53} + 257664 q^{58} - 255420 q^{59} - 4915200 q^{64} + 431016 q^{66} + 126324 q^{67} - 179388 q^{69} - 39600 q^{70} + 20508 q^{71} + 205164 q^{77} + 680100 q^{78} + 650100 q^{81} + 334224 q^{82} - 82608 q^{86} + 1196784 q^{88} - 84960 q^{89} - 345528 q^{91} - 298512 q^{93} + 786300 q^{97} - 809142 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)