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Properties

Label 1050.3.x
Level $1050$
Weight $3$
Character orbit 1050.x
Rep. character $\chi_{1050}(181,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $320$
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.x (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

\( 320 q - 160 q^{4} - 16 q^{7} + 240 q^{9} + O(q^{10}) \) \( 320 q - 160 q^{4} - 16 q^{7} + 240 q^{9} - 120 q^{11} + 24 q^{15} - 320 q^{16} - 88 q^{22} + 72 q^{23} - 88 q^{25} - 72 q^{28} + 120 q^{29} + 96 q^{30} - 116 q^{35} + 480 q^{36} + 208 q^{37} + 72 q^{42} - 640 q^{43} + 160 q^{44} + 120 q^{46} - 80 q^{49} - 96 q^{50} - 456 q^{53} - 96 q^{57} - 224 q^{58} - 192 q^{60} - 132 q^{63} - 640 q^{64} - 320 q^{65} - 160 q^{67} - 312 q^{70} - 160 q^{71} - 320 q^{74} - 240 q^{77} + 192 q^{78} + 320 q^{79} - 720 q^{81} + 464 q^{85} + 480 q^{86} + 224 q^{88} + 380 q^{91} - 96 q^{92} + 192 q^{93} + 680 q^{95} + 64 q^{98} - 240 q^{99} + O(q^{100}) \)

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

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