↑

Properties

Label 1050.3.bi
Level $1050$
Weight $3$
Character orbit 1050.bi
Rep. character $\chi_{1050}(127,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $480$
Sturm bound $720$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.bi (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1050, [\chi])\).

Total New Old
Modular forms 3904 480 3424
Cusp forms 3776 480 3296
Eisenstein series 128 0 128

Trace form

\( 480 q + 8 q^{2} + 16 q^{5} - 16 q^{8} + O(q^{10}) \) \( 480 q + 8 q^{2} + 16 q^{5} - 16 q^{8} - 24 q^{10} + 24 q^{13} + 480 q^{16} - 24 q^{17} - 96 q^{18} - 400 q^{19} - 64 q^{20} - 64 q^{22} - 64 q^{23} + 8 q^{25} - 80 q^{26} + 400 q^{29} + 192 q^{30} + 128 q^{32} + 576 q^{33} + 200 q^{34} - 720 q^{36} - 248 q^{37} + 16 q^{40} + 320 q^{41} + 32 q^{43} - 24 q^{45} - 256 q^{47} + 184 q^{50} + 48 q^{52} + 232 q^{53} + 800 q^{55} - 32 q^{58} - 96 q^{60} - 480 q^{61} - 256 q^{62} + 280 q^{65} - 1120 q^{67} + 48 q^{68} + 112 q^{70} + 48 q^{72} - 472 q^{73} + 288 q^{75} + 224 q^{77} + 800 q^{79} - 64 q^{80} + 1080 q^{81} + 320 q^{82} + 576 q^{83} + 1360 q^{85} - 768 q^{87} - 32 q^{88} - 200 q^{89} - 24 q^{90} + 32 q^{92} - 480 q^{93} - 208 q^{95} - 664 q^{97} - 56 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)