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Properties

Label 1050.3.t
Level $1050$
Weight $3$
Character orbit 1050.t
Rep. character $\chi_{1050}(401,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $204$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
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 204 804
Cusp forms 912 204 708
Eisenstein series 96 0 96

Trace form

\( 204 q + 204 q^{4} - 8 q^{6} - 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 204 q + 204 q^{4} - 8 q^{6} - 6 q^{7} - 4 q^{9} - 68 q^{13} - 408 q^{16} + 8 q^{18} + 62 q^{19} - 6 q^{21} + 16 q^{22} - 8 q^{24} - 132 q^{27} + 130 q^{31} - 126 q^{33} - 16 q^{34} - 16 q^{36} + 70 q^{37} + 50 q^{39} + 16 q^{42} + 20 q^{43} - 48 q^{46} - 126 q^{49} - 114 q^{51} - 68 q^{52} - 104 q^{54} - 56 q^{57} - 16 q^{58} - 356 q^{61} + 48 q^{63} - 1632 q^{64} + 64 q^{66} - 6 q^{67} + 332 q^{69} - 16 q^{72} + 150 q^{73} + 248 q^{76} - 32 q^{78} + 194 q^{79} + 176 q^{81} - 176 q^{82} + 48 q^{84} + 488 q^{87} + 16 q^{88} + 98 q^{91} + 20 q^{93} + 480 q^{94} + 16 q^{96} + 600 q^{97} - 316 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)