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Properties

Label 798.2.bo
Level $798$
Weight $2$
Character orbit 798.bo
Rep. character $\chi_{798}(43,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $120$
Newform subspaces $8$
Sturm bound $320$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 798.bo (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 8 \)
Sturm bound: \(320\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 1008 120 888
Cusp forms 912 120 792
Eisenstein series 96 0 96

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 48 q^{15} + 48 q^{17} - 12 q^{22} + 24 q^{23} + 12 q^{25} - 24 q^{29} + 24 q^{31} - 24 q^{33} - 24 q^{35} + 48 q^{37} - 24 q^{38} + 48 q^{41} - 24 q^{43} - 36 q^{46} - 24 q^{47} - 60 q^{49} - 72 q^{53} - 12 q^{57} + 48 q^{58} - 24 q^{59} - 24 q^{60} + 96 q^{61} - 48 q^{62} - 60 q^{64} + 24 q^{70} - 72 q^{71} - 96 q^{73} - 24 q^{74} + 72 q^{82} + 96 q^{83} - 12 q^{84} + 12 q^{85} + 24 q^{87} - 24 q^{88} + 96 q^{89} + 24 q^{92} + 24 q^{95} + 72 q^{97} + O(q^{100}) \)

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.bo.a 798.bo 19.e $12$ $6.372$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{4}q^{2}-\beta _{11}q^{3}+\beta _{6}q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)
798.2.bo.b 798.bo 19.e $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-9\) \(-6\) $\mathrm{SU}(2)[C_{9}]$ \(q+\beta _{3}q^{2}-\beta _{8}q^{3}+(\beta _{6}-\beta _{11})q^{4}+(-1+\cdots)q^{5}+\cdots\)
798.2.bo.c 798.bo 19.e $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(9\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\beta _{6}-\beta _{10})q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+\cdots\)
798.2.bo.d 798.bo 19.e $12$ $6.372$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(9\) \(6\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{4}q^{2}-\beta _{7}q^{3}+(-\beta _{1}+\beta _{8})q^{4}+\cdots\)
798.2.bo.e 798.bo 19.e $18$ $6.372$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(-6\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{9}q^{2}+\beta _{12}q^{3}+(\beta _{10}-\beta _{11})q^{4}+\cdots\)
798.2.bo.f 798.bo 19.e $18$ $6.372$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{8}q^{2}-\beta _{13}q^{3}+(-\beta _{6}-\beta _{11})q^{4}+\cdots\)
798.2.bo.g 798.bo 19.e $18$ $6.372$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(0\) \(9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{4}q^{2}+(-\beta _{4}-\beta _{8})q^{3}+\beta _{9}q^{4}+\cdots\)
798.2.bo.h 798.bo 19.e $18$ $6.372$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(0\) \(0\) \(6\) \(-9\) $\mathrm{SU}(2)[C_{9}]$ \(q-\beta _{7}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{8})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(798, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(266, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(399, [\chi])\)\(^{\oplus 2}\)