Properties

Label 1050.3.ba
Level $1050$
Weight $3$
Character orbit 1050.ba
Rep. character $\chi_{1050}(29,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
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.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 75 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1952 480 1472
Cusp forms 1888 480 1408
Eisenstein series 64 0 64

Trace form

\( 480 q - 240 q^{4} - 40 q^{9} + O(q^{10}) \) \( 480 q - 240 q^{4} - 40 q^{9} - 16 q^{10} - 40 q^{12} - 44 q^{15} - 480 q^{16} - 120 q^{19} - 40 q^{22} - 208 q^{25} + 56 q^{30} - 240 q^{31} + 240 q^{34} - 80 q^{36} + 80 q^{37} - 120 q^{39} - 32 q^{40} - 408 q^{45} - 120 q^{46} + 80 q^{48} - 3360 q^{49} + 200 q^{51} + 240 q^{54} + 320 q^{55} + 272 q^{60} + 400 q^{61} + 280 q^{63} - 960 q^{64} - 1000 q^{67} + 140 q^{69} + 56 q^{70} + 80 q^{73} - 48 q^{75} + 160 q^{76} - 1240 q^{78} - 240 q^{79} + 400 q^{81} - 1376 q^{85} - 1500 q^{87} + 240 q^{90} + 680 q^{99} + O(q^{100}) \)

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

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