Properties

Label 1050.2.i
Level $1050$
Weight $2$
Character orbit 1050.i
Rep. character $\chi_{1050}(151,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $52$
Newform subspaces $22$
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: \(\Q(\zeta_{3})\)
Newform subspaces: \( 22 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces

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

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