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Properties

Label 1075.6.t
Level $1075$
Weight $6$
Character orbit 1075.t
Rep. character $\chi_{1075}(274,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1968$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 3336 1992 1344
Cusp forms 3264 1968 1296
Eisenstein series 72 24 48

Trace form

\( 1968 q + 5226 q^{4} + 264 q^{6} + 28154 q^{9} + O(q^{10}) \) \( 1968 q + 5226 q^{4} + 264 q^{6} + 28154 q^{9} - 326 q^{11} + 3210 q^{14} - 91218 q^{16} - 586 q^{19} - 11580 q^{21} + 18242 q^{24} + 20150 q^{26} - 42102 q^{29} + 620 q^{31} - 21606 q^{34} + 2483260 q^{36} - 23508 q^{39} - 32570 q^{41} + 176356 q^{44} + 4146 q^{46} - 4552552 q^{49} - 194128 q^{51} + 289894 q^{54} - 384300 q^{56} + 50802 q^{59} - 5408 q^{61} + 883710 q^{64} + 463166 q^{66} - 657926 q^{69} + 160674 q^{71} - 498788 q^{74} + 637974 q^{76} - 71000 q^{79} - 824930 q^{81} - 840948 q^{84} - 885486 q^{86} - 272416 q^{89} + 263956 q^{91} + 553222 q^{94} + 1973318 q^{96} - 1713390 q^{99} + O(q^{100}) \)

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

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