Properties

Label 1050.3.q
Level $1050$
Weight $3$
Character orbit 1050.q
Rep. character $\chi_{1050}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $96$
Newform subspaces $5$
Sturm bound $720$
Trace bound $14$

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Defining parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1050.q (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(720\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(11\)

Dimensions

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

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

Trace form

\( 96q + 96q^{4} - 144q^{9} + O(q^{10}) \) \( 96q + 96q^{4} - 144q^{9} - 56q^{11} + 32q^{14} - 192q^{16} - 156q^{19} - 12q^{21} - 192q^{26} - 192q^{29} - 24q^{31} - 576q^{36} - 36q^{39} + 112q^{44} + 16q^{46} + 244q^{49} + 48q^{51} + 128q^{56} - 1008q^{59} + 204q^{61} - 768q^{64} - 32q^{71} + 512q^{74} - 136q^{79} - 432q^{81} - 48q^{84} - 368q^{86} + 96q^{89} - 1612q^{91} - 576q^{94} + 336q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1050.3.q.a \(8\) \(28.610\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{5}q^{2}+(\zeta_{24}-2\zeta_{24}^{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1050.3.q.b \(16\) \(28.610\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(-\beta _{1}-\beta _{9})q^{3}+(2+2\beta _{3}+\cdots)q^{4}+\cdots\)
1050.3.q.c \(16\) \(28.610\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{13}q^{2}+(\beta _{1}+2\beta _{8})q^{3}-2\beta _{6}q^{4}+\cdots\)
1050.3.q.d \(24\) \(28.610\) None \(0\) \(0\) \(0\) \(0\)
1050.3.q.e \(32\) \(28.610\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)