↑

Properties

Label 798.2.j
Level $798$
Weight $2$
Character orbit 798.j
Rep. character $\chi_{798}(457,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $12$
Sturm bound $320$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(320\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(798, [\chi])\).

Total New Old
Modular forms 336 48 288
Cusp forms 304 48 256
Eisenstein series 32 0 32

Trace form

\( 48 q - 24 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{9} + O(q^{10}) \) \( 48 q - 24 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{7} - 24 q^{9} + 4 q^{10} + 4 q^{11} - 8 q^{15} - 24 q^{16} - 8 q^{17} - 4 q^{19} - 8 q^{20} - 8 q^{22} + 4 q^{23} - 4 q^{24} - 16 q^{25} + 4 q^{28} - 32 q^{29} + 20 q^{31} + 4 q^{33} + 36 q^{35} + 48 q^{36} + 24 q^{37} + 4 q^{40} + 16 q^{41} - 4 q^{42} + 8 q^{43} + 4 q^{44} + 4 q^{45} - 8 q^{46} - 28 q^{47} - 8 q^{49} + 64 q^{50} + 8 q^{51} - 16 q^{53} - 4 q^{54} - 64 q^{55} - 36 q^{58} - 16 q^{59} + 4 q^{60} - 52 q^{61} - 48 q^{62} + 4 q^{63} + 48 q^{64} + 16 q^{65} - 16 q^{66} + 24 q^{67} - 8 q^{68} - 32 q^{69} + 36 q^{70} - 80 q^{71} + 4 q^{73} - 16 q^{74} + 16 q^{75} + 8 q^{76} + 32 q^{77} + 16 q^{78} + 20 q^{79} + 4 q^{80} - 24 q^{81} + 16 q^{82} + 56 q^{83} - 32 q^{85} + 40 q^{86} + 28 q^{87} + 4 q^{88} + 32 q^{89} - 8 q^{90} + 48 q^{91} - 8 q^{92} + 4 q^{95} - 4 q^{96} + 40 q^{97} + 16 q^{98} - 8 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(798, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
798.2.j.a 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.b 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.c 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.d 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.e 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.f 798.j 7.c $2$ $6.372$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
798.2.j.g 798.j 7.c $4$ $6.372$ \(\Q(\zeta_{12})\) None \(-2\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}+(1-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
798.2.j.h 798.j 7.c $4$ $6.372$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(2\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
798.2.j.i 798.j 7.c $6$ $6.372$ 6.0.4406832.1 None \(-3\) \(-3\) \(5\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{2}+(-1+\beta _{4})q^{3}+(-1+\beta _{4}+\cdots)q^{4}+\cdots\)
798.2.j.j 798.j 7.c $6$ $6.372$ 6.0.4406832.1 None \(3\) \(3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(1-\beta _{4})q^{3}+(-1+\beta _{4})q^{4}+\cdots\)
798.2.j.k 798.j 7.c $8$ $6.372$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
798.2.j.l 798.j 7.c $8$ $6.372$ 8.0.856615824.2 None \(4\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(798, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)