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Properties

Label 1045.6.bg
Level $1045$
Weight $6$
Character orbit 1045.bg
Rep. character $\chi_{1045}(87,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2384$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2416 2416 0
Cusp forms 2384 2384 0
Eisenstein series 32 32 0

Trace form

\( 2384 q - 4 q^{3} + 40 q^{5} + O(q^{10}) \) \( 2384 q - 4 q^{3} + 40 q^{5} - 56 q^{11} - 2216 q^{12} - 4 q^{15} + 299000 q^{16} + 19072 q^{20} - 2406 q^{22} + 5100 q^{23} - 664 q^{25} - 10592 q^{26} - 1960 q^{27} - 32 q^{31} + 3856 q^{33} + 1527640 q^{36} - 52464 q^{37} + 107392 q^{38} + 110564 q^{42} - 17272 q^{45} + 54336 q^{47} + 37396 q^{48} - 31816 q^{53} + 7020 q^{55} - 185376 q^{56} - 72632 q^{58} - 19716 q^{60} + 53500 q^{66} - 86420 q^{67} - 59500 q^{70} - 8 q^{71} - 152432 q^{75} + 131980 q^{77} - 280200 q^{78} + 39672 q^{80} + 7244160 q^{81} - 35864 q^{82} + 865912 q^{86} + 476536 q^{88} - 486648 q^{91} - 509828 q^{92} + 210136 q^{93} - 179348 q^{97} + O(q^{100}) \)

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.