Properties

Label 1050.3.k
Level $1050$
Weight $3$
Character orbit 1050.k
Rep. character $\chi_{1050}(293,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $192$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 105 \)
Character field: \(\Q(i)\)
Sturm bound: \(720\)

Dimensions

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

Total New Old
Modular forms 1008 192 816
Cusp forms 912 192 720
Eisenstein series 96 0 96

Trace form

\( 192 q + 8 q^{7} + O(q^{10}) \) \( 192 q + 8 q^{7} - 768 q^{16} - 32 q^{18} - 48 q^{21} + 80 q^{22} + 16 q^{28} + 160 q^{36} - 64 q^{37} + 64 q^{42} + 64 q^{43} + 192 q^{46} - 336 q^{51} - 584 q^{57} - 224 q^{58} - 240 q^{63} - 64 q^{67} + 64 q^{72} + 128 q^{78} - 304 q^{81} + 160 q^{88} + 88 q^{91} + 840 q^{93} + O(q^{100}) \)

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

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