Properties

Label 1050.3.bu
Level $1050$
Weight $3$
Character orbit 1050.bu
Rep. character $\chi_{1050}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1280$
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.bu (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 7808 1280 6528
Cusp forms 7552 1280 6272
Eisenstein series 256 0 256

Trace form

\( 1280 q + 8 q^{5} - 16 q^{7} + O(q^{10}) \) \( 1280 q + 8 q^{5} - 16 q^{7} - 16 q^{10} - 48 q^{15} - 640 q^{16} - 448 q^{17} + 64 q^{22} - 32 q^{23} - 40 q^{25} - 32 q^{28} - 800 q^{29} + 192 q^{30} - 24 q^{33} + 400 q^{35} - 1920 q^{36} + 8 q^{37} + 64 q^{38} + 48 q^{42} - 464 q^{43} + 440 q^{47} + 688 q^{53} + 208 q^{55} - 192 q^{57} + 208 q^{58} - 800 q^{59} + 96 q^{62} - 120 q^{63} + 136 q^{65} - 128 q^{67} - 224 q^{68} - 32 q^{70} - 136 q^{73} + 96 q^{75} + 1160 q^{77} + 192 q^{78} - 32 q^{80} - 1440 q^{81} - 512 q^{82} - 128 q^{83} - 464 q^{85} + 144 q^{87} - 96 q^{88} - 192 q^{92} - 192 q^{93} - 760 q^{95} - 160 q^{97} + 128 q^{98} + O(q^{100}) \)

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

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