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Properties

Label 1045.6.bd
Level $1045$
Weight $6$
Character orbit 1045.bd
Rep. character $\chi_{1045}(12,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2000$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
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 2000 416
Cusp forms 2384 2000 384
Eisenstein series 32 0 32

Trace form

\( 2000 q - 360 q^{6} + O(q^{10}) \) \( 2000 q - 360 q^{6} + 6516 q^{15} + 252280 q^{16} + 1068 q^{17} + 2160 q^{21} - 14232 q^{23} - 6492 q^{28} + 47232 q^{32} + 18180 q^{35} - 1283040 q^{36} - 18588 q^{38} - 102528 q^{40} - 8640 q^{43} - 91528 q^{45} + 24416 q^{47} + 40236 q^{48} - 182400 q^{51} + 20204 q^{57} + 306336 q^{58} - 140544 q^{60} - 214000 q^{61} - 228560 q^{63} - 136704 q^{68} - 1326228 q^{72} + 133184 q^{73} - 164520 q^{76} + 1116840 q^{78} + 122708 q^{80} + 6465880 q^{81} + 83920 q^{82} + 271352 q^{83} - 1354440 q^{86} - 736112 q^{87} + 1781940 q^{90} - 336000 q^{91} + 688964 q^{92} + 213168 q^{93} + 319992 q^{95} - 534240 q^{96} + 247356 q^{97} + 45504 q^{98} + O(q^{100}) \)

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

\( S_{6}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 2}\)