Properties

Label 1050.3.be
Level $1050$
Weight $3$
Character orbit 1050.be
Rep. character $\chi_{1050}(143,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $384$
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.be (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 2016 384 1632
Cusp forms 1824 384 1440
Eisenstein series 192 0 192

Trace form

\( 384 q - 8 q^{7} + O(q^{10}) \) \( 384 q - 8 q^{7} + 768 q^{16} + 32 q^{18} - 144 q^{21} - 32 q^{22} - 16 q^{28} - 60 q^{33} - 64 q^{36} + 64 q^{37} + 224 q^{42} - 64 q^{43} + 96 q^{46} + 336 q^{51} + 536 q^{57} - 112 q^{58} - 840 q^{61} + 324 q^{63} - 32 q^{67} - 64 q^{72} + 1248 q^{73} + 256 q^{78} + 256 q^{81} + 384 q^{82} + 612 q^{87} + 32 q^{88} + 968 q^{91} + 372 q^{93} + 192 q^{96} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)