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Properties

Label 1050.3.bq
Level $1050$
Weight $3$
Character orbit 1050.bq
Rep. character $\chi_{1050}(31,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $640$
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.bq (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
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 640 3264
Cusp forms 3776 640 3136
Eisenstein series 128 0 128

Trace form

\( 640 q + 160 q^{4} - 12 q^{5} + 16 q^{7} - 240 q^{9} + O(q^{10}) \) \( 640 q + 160 q^{4} - 12 q^{5} + 16 q^{7} - 240 q^{9} + 24 q^{10} - 60 q^{11} - 24 q^{15} + 320 q^{16} + 16 q^{22} + 72 q^{23} - 32 q^{25} - 72 q^{28} + 240 q^{29} - 96 q^{30} + 180 q^{31} + 72 q^{33} + 248 q^{35} + 960 q^{36} + 8 q^{37} + 192 q^{38} - 48 q^{40} - 72 q^{42} + 1072 q^{43} + 80 q^{44} - 36 q^{45} - 120 q^{46} + 312 q^{47} + 80 q^{49} + 192 q^{50} + 456 q^{53} - 192 q^{57} + 176 q^{58} + 720 q^{59} - 96 q^{60} - 360 q^{61} + 60 q^{63} - 1280 q^{64} - 220 q^{65} + 64 q^{67} - 96 q^{70} - 320 q^{71} - 24 q^{73} + 320 q^{74} + 144 q^{75} - 120 q^{77} - 192 q^{78} - 200 q^{79} + 48 q^{80} + 720 q^{81} + 1536 q^{82} + 2488 q^{85} + 240 q^{86} + 64 q^{88} + 700 q^{91} + 192 q^{92} - 192 q^{93} - 480 q^{94} - 548 q^{95} - 64 q^{98} + 240 q^{99} + O(q^{100}) \)

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

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