Properties

Label 1050.3.v
Level $1050$
Weight $3$
Character orbit 1050.v
Rep. character $\chi_{1050}(139,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.v (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 320 1632
Cusp forms 1888 320 1568
Eisenstein series 64 0 64

Trace form

\( 320 q + 160 q^{4} - 240 q^{9} + O(q^{10}) \) \( 320 q + 160 q^{4} - 240 q^{9} + 120 q^{11} + 24 q^{15} - 320 q^{16} - 40 q^{22} - 200 q^{23} - 24 q^{25} - 40 q^{28} + 120 q^{29} + 96 q^{30} - 212 q^{35} + 480 q^{36} - 120 q^{42} + 160 q^{44} - 120 q^{46} - 80 q^{49} + 96 q^{50} + 120 q^{53} + 192 q^{60} + 180 q^{63} + 640 q^{64} - 368 q^{65} - 24 q^{70} + 160 q^{71} - 320 q^{74} + 320 q^{79} - 720 q^{81} - 480 q^{86} - 320 q^{88} - 380 q^{91} - 280 q^{95} + 320 q^{98} - 240 q^{99} + O(q^{100}) \)

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

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