Properties

Label 1050.3.bt
Level $1050$
Weight $3$
Character orbit 1050.bt
Rep. character $\chi_{1050}(17,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $2560$
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.bt (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 525 \)
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 2560 5248
Cusp forms 7552 2560 4992
Eisenstein series 256 0 256

Trace form

\( 2560 q - 8 q^{7} + O(q^{10}) \) \( 2560 q - 8 q^{7} - 48 q^{10} - 24 q^{15} - 1280 q^{16} + 32 q^{18} - 192 q^{22} + 32 q^{25} + 64 q^{28} - 48 q^{30} - 60 q^{33} + 64 q^{37} - 400 q^{39} + 224 q^{42} - 64 q^{43} - 372 q^{45} - 744 q^{57} - 112 q^{58} - 32 q^{60} - 776 q^{63} - 32 q^{67} - 320 q^{70} - 64 q^{72} + 1248 q^{73} - 384 q^{75} + 256 q^{78} - 1536 q^{82} + 600 q^{84} + 304 q^{85} + 612 q^{87} + 32 q^{88} + 372 q^{93} + O(q^{100}) \)

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

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