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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1050.2.i.a 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.b 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.c 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.d 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.e 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.f 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.g 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.h 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.i 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.j 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.k 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.l 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.m 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.n 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.o 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.p 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.q 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.r 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.s 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.t 1050.i 7.c $2$ $8.384$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
1050.2.i.u 1050.i 7.c $6$ $8.384$ 6.0.21870000.1 None \(-3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
1050.2.i.v 1050.i 7.c $6$ $8.384$ 6.0.21870000.1 None \(3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 3}\)