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Properties

Label 1045.6.cc
Level $1045$
Weight $6$
Character orbit 1045.cc
Rep. character $\chi_{1045}(67,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $6000$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.cc (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 7248 6000 1248
Cusp forms 7152 6000 1152
Eisenstein series 96 0 96

Trace form

\( 6000 q + 1080 q^{6} + O(q^{10}) \) \( 6000 q + 1080 q^{6} - 6516 q^{15} - 360 q^{16} - 3204 q^{17} + 4320 q^{21} + 42696 q^{23} - 38952 q^{28} - 47232 q^{32} - 25884 q^{35} - 38880 q^{36} + 82476 q^{38} + 102528 q^{40} + 143904 q^{43} - 11916 q^{45} - 195768 q^{47} + 80472 q^{48} + 182400 q^{51} - 163740 q^{57} - 459504 q^{58} - 281088 q^{60} + 65040 q^{61} + 172944 q^{63} + 901620 q^{65} - 467112 q^{72} + 453120 q^{76} + 570264 q^{78} - 848508 q^{80} - 570720 q^{81} + 1329900 q^{82} + 631560 q^{86} - 328980 q^{90} + 1186320 q^{91} + 57396 q^{92} - 639504 q^{93} + 629352 q^{95} + 2004480 q^{96} + 494712 q^{97} - 45504 q^{98} + O(q^{100}) \)

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

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