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Properties

Label 1075.6.g
Level $1075$
Weight $6$
Character orbit 1075.g
Rep. character $\chi_{1075}(257,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $656$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.g (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(i)\)
Sturm bound: \(660\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1075, [\chi])\).

Total New Old
Modular forms 1112 664 448
Cusp forms 1088 656 432
Eisenstein series 24 8 16

Trace form

\( 656 q - 328 q^{6} + O(q^{10}) \) \( 656 q - 328 q^{6} - 8 q^{11} - 1044 q^{13} - 161832 q^{16} + 768 q^{17} - 17568 q^{21} - 1412 q^{23} + 32192 q^{31} + 759480 q^{36} + 106532 q^{38} + 85432 q^{41} - 16240 q^{43} - 19228 q^{47} + 135712 q^{52} + 52684 q^{53} - 302456 q^{56} - 53604 q^{57} + 116864 q^{58} + 10144 q^{66} - 136924 q^{67} + 474292 q^{68} - 430508 q^{78} - 4475512 q^{81} + 59420 q^{83} + 571736 q^{86} - 274680 q^{87} + 416552 q^{92} + 268576 q^{96} + 282220 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1075, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(1075, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1075, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(215, [\chi])\)\(^{\oplus 2}\)