Properties

Label 1848.2.bg
Level $1848$
Weight $2$
Character orbit 1848.bg
Rep. character $\chi_{1848}(529,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $80$
Newform subspaces $11$
Sturm bound $768$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1848.bg (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 11 \)
Sturm bound: \(768\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1848, [\chi])\).

Total New Old
Modular forms 800 80 720
Cusp forms 736 80 656
Eisenstein series 64 0 64

Trace form

\( 80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{3} - 4 q^{7} - 40 q^{9} - 8 q^{13} + 4 q^{19} + 8 q^{21} - 40 q^{25} + 8 q^{27} + 4 q^{31} + 4 q^{33} + 16 q^{35} + 4 q^{39} + 8 q^{43} - 12 q^{49} + 8 q^{51} + 32 q^{53} - 8 q^{57} - 16 q^{59} - 8 q^{61} - 4 q^{63} + 32 q^{65} + 4 q^{67} - 24 q^{69} - 32 q^{71} - 12 q^{73} - 36 q^{75} + 44 q^{79} - 40 q^{81} - 32 q^{83} - 32 q^{85} + 28 q^{91} + 4 q^{93} - 32 q^{95} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1848, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1848.2.bg.a 1848.bg 7.c $2$ $14.756$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1848.2.bg.b 1848.bg 7.c $2$ $14.756$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots\)
1848.2.bg.c 1848.bg 7.c $4$ $14.756$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(0\) \(-2\) \(-1\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{3}-\beta _{1}q^{5}+(-2-\beta _{2}+\cdots)q^{7}+\cdots\)
1848.2.bg.d 1848.bg 7.c $6$ $14.756$ 6.0.1714608.1 None \(0\) \(-3\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{3}+(-2\beta _{1}-\beta _{2}-\beta _{4}+\cdots)q^{5}+\cdots\)
1848.2.bg.e 1848.bg 7.c $6$ $14.756$ 6.0.4406832.1 None \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4})q^{3}+(-\beta _{1}+\beta _{2}+\beta _{5})q^{5}+\cdots\)
1848.2.bg.f 1848.bg 7.c $8$ $14.756$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-4\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{3}-\beta _{5}q^{5}+(-\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1848.2.bg.g 1848.bg 7.c $8$ $14.756$ 8.0.\(\cdots\).13 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{3}+(\beta _{4}+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1848.2.bg.h 1848.bg 7.c $10$ $14.756$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(0\) \(-5\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{6}q^{3}+(\beta _{5}+\beta _{8})q^{5}+(\beta _{4}-\beta _{9})q^{7}+\cdots\)
1848.2.bg.i 1848.bg 7.c $10$ $14.756$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(5\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{6}q^{3}+\beta _{9}q^{5}+(-\beta _{2}+\beta _{5}-\beta _{9})q^{7}+\cdots\)
1848.2.bg.j 1848.bg 7.c $12$ $14.756$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{6})q^{3}+(\beta _{1}+\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1848.2.bg.k 1848.bg 7.c $12$ $14.756$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{5})q^{3}+(-\beta _{4}-\beta _{11})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1848, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1848, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(308, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(616, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(924, [\chi])\)\(^{\oplus 2}\)