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Properties

Label 1050.3.r
Level $1050$
Weight $3$
Character orbit 1050.r
Rep. character $\chi_{1050}(149,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $192$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.r (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1008 192 816
Cusp forms 912 192 720
Eisenstein series 96 0 96

Trace form

\( 192 q - 192 q^{4} - 16 q^{6} + 8 q^{9} + O(q^{10}) \) \( 192 q - 192 q^{4} - 16 q^{6} + 8 q^{9} - 384 q^{16} + 4 q^{19} + 116 q^{21} + 16 q^{24} + 16 q^{31} - 32 q^{36} + 236 q^{39} + 32 q^{46} + 228 q^{49} + 160 q^{51} + 112 q^{54} - 468 q^{61} + 1536 q^{64} + 160 q^{66} - 632 q^{69} - 16 q^{76} + 520 q^{79} - 368 q^{81} + 40 q^{84} + 516 q^{91} - 640 q^{94} + 32 q^{96} + 816 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)