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Properties

Label 1428.2.q
Level $1428$
Weight $2$
Character orbit 1428.q
Rep. character $\chi_{1428}(205,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $44$
Newform subspaces $8$
Sturm bound $576$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1428 = 2^{2} \cdot 3 \cdot 7 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1428.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(576\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1428, [\chi])\).

Total New Old
Modular forms 600 44 556
Cusp forms 552 44 508
Eisenstein series 48 0 48

Trace form

\( 44 q - 2 q^{3} - 6 q^{7} - 22 q^{9} + O(q^{10}) \) \( 44 q - 2 q^{3} - 6 q^{7} - 22 q^{9} + 8 q^{11} - 4 q^{13} - 8 q^{15} + 6 q^{19} + 8 q^{21} + 8 q^{23} - 14 q^{25} + 4 q^{27} - 16 q^{29} + 14 q^{31} + 4 q^{33} - 40 q^{35} - 2 q^{37} + 6 q^{39} + 8 q^{41} - 52 q^{43} + 20 q^{47} + 18 q^{49} + 4 q^{53} + 32 q^{55} - 20 q^{57} - 32 q^{61} + 6 q^{63} + 28 q^{65} + 6 q^{67} + 24 q^{71} - 34 q^{73} - 14 q^{75} + 24 q^{77} + 30 q^{79} - 22 q^{81} - 48 q^{83} + 4 q^{87} - 4 q^{89} + 10 q^{91} + 2 q^{93} - 8 q^{95} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1428, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1428.2.q.a 1428.q 7.c $2$ $11.403$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}-\zeta_{6}q^{9}+\cdots\)
1428.2.q.b 1428.q 7.c $2$ $11.403$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots\)
1428.2.q.c 1428.q 7.c $2$ $11.403$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1428.2.q.d 1428.q 7.c $2$ $11.403$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1428.2.q.e 1428.q 7.c $8$ $11.403$ 8.0.447703281.1 None \(0\) \(-4\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}+(\beta _{1}-\beta _{4})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
1428.2.q.f 1428.q 7.c $8$ $11.403$ 8.0.1767277521.3 None \(0\) \(4\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{3}+(-1+\beta _{1}-\beta _{4}+\beta _{6})q^{5}+\cdots\)
1428.2.q.g 1428.q 7.c $8$ $11.403$ 8.0.1405125225.1 None \(0\) \(4\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}+(1-\beta _{4}+\beta _{6}-\beta _{7})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1428.2.q.h 1428.q 7.c $12$ $11.403$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{3}+\beta _{1}q^{5}+(-\beta _{7}+\beta _{9}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1428, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1428, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(119, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(238, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(357, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(476, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(714, [\chi])\)\(^{\oplus 2}\)