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Properties

Label 1075.6.j
Level $1075$
Weight $6$
Character orbit 1075.j
Rep. character $\chi_{1075}(49,\cdot)$
Character field $\Q(\zeta_{6})$
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.j (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{6})\)
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

\( 656 q - 10424 q^{4} - 146 q^{6} + 26626 q^{9} + O(q^{10}) \) \( 656 q - 10424 q^{4} - 146 q^{6} + 26626 q^{9} - 324 q^{11} - 1334 q^{14} + 161016 q^{16} - 4032 q^{19} - 8176 q^{21} + 23212 q^{24} + 19966 q^{26} - 4006 q^{29} - 1582 q^{31} - 3062 q^{34} - 462670 q^{36} + 22288 q^{39} - 1128 q^{41} + 37392 q^{44} - 76108 q^{46} + 769838 q^{49} - 59104 q^{51} - 259048 q^{54} - 34106 q^{56} - 72632 q^{59} + 117698 q^{61} - 2566624 q^{64} + 198732 q^{66} - 42662 q^{69} + 59198 q^{71} - 202750 q^{74} + 247630 q^{76} - 38762 q^{79} - 2108800 q^{81} - 189128 q^{84} - 534390 q^{86} - 325984 q^{89} - 72328 q^{91} + 1322484 q^{94} - 449332 q^{96} + 345344 q^{99} + O(q^{100}) \)

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

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