Properties

Label 1050.2.i
Level 1050
Weight 2
Character orbit i
Rep. character \(\chi_{1050}(151,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 52
Newforms 22
Sturm bound 480
Trace bound 13

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Defining parameters

Level: \( N \) = \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1050.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 22 \)
Sturm bound: \(480\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1050, [\chi])\).

Total New Old
Modular forms 528 52 476
Cusp forms 432 52 380
Eisenstein series 96 0 96

Trace form

\(52q \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(52q \) \(\mathstrut -\mathstrut 26q^{4} \) \(\mathstrut +\mathstrut 4q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 26q^{16} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 8q^{19} \) \(\mathstrut +\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 12q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut -\mathstrut 2q^{24} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 6q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 26q^{31} \) \(\mathstrut +\mathstrut 6q^{33} \) \(\mathstrut +\mathstrut 24q^{34} \) \(\mathstrut +\mathstrut 52q^{36} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 4q^{38} \) \(\mathstrut -\mathstrut 10q^{42} \) \(\mathstrut -\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 28q^{47} \) \(\mathstrut +\mathstrut 22q^{49} \) \(\mathstrut +\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut -\mathstrut 36q^{53} \) \(\mathstrut -\mathstrut 2q^{54} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 36q^{61} \) \(\mathstrut -\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 52q^{64} \) \(\mathstrut -\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 4q^{67} \) \(\mathstrut -\mathstrut 12q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 56q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 28q^{74} \) \(\mathstrut +\mathstrut 16q^{76} \) \(\mathstrut +\mathstrut 52q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 26q^{81} \) \(\mathstrut +\mathstrut 16q^{82} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 16q^{84} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 14q^{87} \) \(\mathstrut -\mathstrut 6q^{88} \) \(\mathstrut +\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 32q^{91} \) \(\mathstrut +\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 4q^{93} \) \(\mathstrut -\mathstrut 8q^{94} \) \(\mathstrut -\mathstrut 2q^{96} \) \(\mathstrut +\mathstrut 52q^{97} \) \(\mathstrut -\mathstrut 24q^{98} \) \(\mathstrut -\mathstrut 16q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1050.2.i.a \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.b \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.c \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.d \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.e \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.f \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.g \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.h \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.i \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(4\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.j \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(5\) \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.k \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-5\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.l \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.m \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.n \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.o \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.p \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(4\) \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.q \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.r \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.s \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.t \(2\) \(8.384\) \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(5\) \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.u \(6\) \(8.384\) 6.0.21870000.1 None \(-3\) \(-3\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1050.2.i.v \(6\) \(8.384\) 6.0.21870000.1 None \(3\) \(3\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces

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