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Properties

Label 1050.3.bo
Level $1050$
Weight $3$
Character orbit 1050.bo
Rep. character $\chi_{1050}(179,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1280$
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.bo (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 3904 1280 2624
Cusp forms 3776 1280 2496
Eisenstein series 128 0 128

Trace form

\( 1280 q + 320 q^{4} + O(q^{10}) \) \( 1280 q + 320 q^{4} + 8 q^{10} + 76 q^{15} + 640 q^{16} + 60 q^{21} + 80 q^{22} - 12 q^{25} - 840 q^{27} + 40 q^{28} + 8 q^{30} + 60 q^{31} - 50 q^{33} - 20 q^{39} + 16 q^{40} + 54 q^{45} - 120 q^{46} + 120 q^{49} + 120 q^{51} - 616 q^{55} + 4 q^{60} + 550 q^{63} - 2560 q^{64} + 160 q^{66} + 420 q^{69} - 816 q^{70} + 160 q^{73} + 762 q^{75} + 280 q^{79} - 40 q^{81} - 180 q^{84} - 1672 q^{85} + 160 q^{88} - 512 q^{90} + 340 q^{91} + 160 q^{94} - 40 q^{97} + 320 q^{99} + O(q^{100}) \)

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

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