Properties

Label 1075.6.p
Level $1075$
Weight $6$
Character orbit 1075.p
Rep. character $\chi_{1075}(7,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1312$
Sturm bound $660$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.p (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 215 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 2224 1328 896
Cusp forms 2176 1312 864
Eisenstein series 48 16 32

Trace form

\( 1312 q + 6 q^{3} - 164 q^{6} - 348 q^{7} + O(q^{10}) \) \( 1312 q + 6 q^{3} - 164 q^{6} - 348 q^{7} - 16 q^{11} + 732 q^{12} + 1050 q^{13} - 332784 q^{16} + 384 q^{17} - 11184 q^{18} + 17544 q^{21} - 706 q^{23} - 12 q^{26} - 28602 q^{28} - 3164 q^{31} - 2712 q^{33} - 856644 q^{36} + 6 q^{37} - 51740 q^{38} - 148336 q^{41} - 43988 q^{43} - 160152 q^{46} + 102532 q^{47} + 45006 q^{48} - 32752 q^{52} - 78928 q^{53} - 81988 q^{56} - 28260 q^{57} + 58432 q^{58} + 35448 q^{61} - 42936 q^{62} - 14136 q^{63} - 255388 q^{66} + 136930 q^{67} - 406894 q^{68} + 359628 q^{71} + 720042 q^{72} + 327840 q^{73} - 118764 q^{76} - 29088 q^{77} + 330680 q^{78} + 3903340 q^{81} + 184492 q^{83} - 1118948 q^{86} - 964320 q^{87} + 833448 q^{91} - 311150 q^{92} - 419142 q^{93} + 1049468 q^{96} + 564440 q^{97} - 19578 q^{98} + O(q^{100}) \)

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

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