Properties

Label 1050.3.p
Level $1050$
Weight $3$
Character orbit 1050.p
Rep. character $\chi_{1050}(451,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $100$
Newform subspaces $9$
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.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(720\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(11\), \(17\)

Dimensions

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

Total New Old
Modular forms 1008 100 908
Cusp forms 912 100 812
Eisenstein series 96 0 96

Trace form

\( 100 q + 6 q^{3} - 100 q^{4} + 6 q^{7} + 150 q^{9} + O(q^{10}) \) \( 100 q + 6 q^{3} - 100 q^{4} + 6 q^{7} + 150 q^{9} + 12 q^{11} - 12 q^{12} - 8 q^{14} - 200 q^{16} - 48 q^{17} + 114 q^{19} - 12 q^{21} + 96 q^{22} - 24 q^{23} - 96 q^{26} - 72 q^{28} - 128 q^{29} - 162 q^{31} + 36 q^{33} - 600 q^{36} + 30 q^{37} + 216 q^{38} + 42 q^{39} + 72 q^{42} + 140 q^{43} + 24 q^{44} + 104 q^{46} + 180 q^{47} - 86 q^{49} + 12 q^{52} - 184 q^{53} + 80 q^{56} - 276 q^{57} + 80 q^{58} + 24 q^{59} - 588 q^{61} - 90 q^{63} + 800 q^{64} + 174 q^{67} + 96 q^{68} - 360 q^{71} + 390 q^{73} + 80 q^{74} - 274 q^{79} - 450 q^{81} - 336 q^{82} + 108 q^{84} + 88 q^{86} - 96 q^{88} - 168 q^{89} + 166 q^{91} + 96 q^{92} + 150 q^{93} - 408 q^{94} - 384 q^{98} + 72 q^{99} + O(q^{100}) \)

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.p.a $4$ $28.610$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-6\) \(0\) \(10\) \(q-\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
1050.3.p.b $8$ $28.610$ 8.0.3317760000.3 None \(0\) \(-12\) \(0\) \(0\) \(q+(-\beta _{2}-\beta _{4})q^{2}+(-1-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1050.3.p.c $8$ $28.610$ 8.0.\(\cdots\).6 None \(0\) \(-12\) \(0\) \(0\) \(q+(\beta _{2}-\beta _{6})q^{2}+(-1-\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1050.3.p.d $8$ $28.610$ 8.0.\(\cdots\).6 None \(0\) \(12\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{6})q^{2}+(1+\beta _{3})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1050.3.p.e $12$ $28.610$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-18\) \(0\) \(-8\) \(q+(-\beta _{4}+\beta _{5})q^{2}+(-2+\beta _{3})q^{3}-2\beta _{3}q^{4}+\cdots\)
1050.3.p.f $12$ $28.610$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(18\) \(0\) \(8\) \(q+(\beta _{4}-\beta _{5})q^{2}+(2-\beta _{3})q^{3}-2\beta _{3}q^{4}+\cdots\)
1050.3.p.g $16$ $28.610$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-24\) \(0\) \(12\) \(q+(-\beta _{3}+\beta _{8})q^{2}+(-1+\beta _{7})q^{3}+(-2+\cdots)q^{4}+\cdots\)
1050.3.p.h $16$ $28.610$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(24\) \(0\) \(-12\) \(q+(\beta _{3}-\beta _{8})q^{2}+(1-\beta _{7})q^{3}+(-2-2\beta _{7}+\cdots)q^{4}+\cdots\)
1050.3.p.i $16$ $28.610$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(24\) \(0\) \(-4\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(2+\beta _{3})q^{3}+2\beta _{3}q^{4}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)