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Properties

Label 1098.2.e
Level $1098$
Weight $2$
Character orbit 1098.e
Rep. character $\chi_{1098}(367,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
Newform subspaces $7$
Sturm bound $372$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 1098 = 2 \cdot 3^{2} \cdot 61 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1098.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(372\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1098, [\chi])\).

Total New Old
Modular forms 380 120 260
Cusp forms 364 120 244
Eisenstein series 16 0 16

Trace form

\( 120 q + 2 q^{2} + 6 q^{3} - 60 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{8} - 10 q^{9} + O(q^{10}) \) \( 120 q + 2 q^{2} + 6 q^{3} - 60 q^{4} - 4 q^{5} + 2 q^{6} - 4 q^{8} - 10 q^{9} - 6 q^{11} + 16 q^{15} - 60 q^{16} + 12 q^{17} + 4 q^{18} + 12 q^{19} - 4 q^{20} - 32 q^{21} - 6 q^{22} + 8 q^{23} + 2 q^{24} - 72 q^{25} - 8 q^{26} + 12 q^{27} + 28 q^{29} - 12 q^{30} - 12 q^{31} + 2 q^{32} + 10 q^{33} - 6 q^{34} - 40 q^{35} + 2 q^{36} + 24 q^{37} - 2 q^{38} + 20 q^{39} - 18 q^{41} + 32 q^{42} - 6 q^{43} + 12 q^{44} + 12 q^{45} - 16 q^{47} - 6 q^{48} - 60 q^{49} + 14 q^{50} - 30 q^{51} - 22 q^{54} - 30 q^{57} + 12 q^{58} + 6 q^{59} - 8 q^{60} + 48 q^{62} - 48 q^{63} + 120 q^{64} - 48 q^{65} - 18 q^{67} - 6 q^{68} - 24 q^{69} + 12 q^{70} + 80 q^{71} + 10 q^{72} + 12 q^{73} - 12 q^{74} + 30 q^{75} - 6 q^{76} + 24 q^{78} - 12 q^{79} + 8 q^{80} + 30 q^{81} + 12 q^{82} + 44 q^{83} + 4 q^{84} - 24 q^{85} - 14 q^{86} - 64 q^{87} - 6 q^{88} - 112 q^{89} + 36 q^{90} + 48 q^{91} + 8 q^{92} + 12 q^{93} + 36 q^{95} - 4 q^{96} - 18 q^{97} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1098, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1098.2.e.a 1098.e 9.c $2$ $8.768$ \(\Q(\sqrt{-3}) \) None 1098.2.e.a \(1\) \(-3\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1098.2.e.b 1098.e 9.c $2$ $8.768$ \(\Q(\sqrt{-3}) \) None 1098.2.e.b \(1\) \(-3\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1098.2.e.c 1098.e 9.c $2$ $8.768$ \(\Q(\sqrt{-3}) \) None 1098.2.e.c \(1\) \(-3\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
1098.2.e.d 1098.e 9.c $22$ $8.768$ None 1098.2.e.d \(11\) \(7\) \(-9\) \(8\) $\mathrm{SU}(2)[C_{3}]$
1098.2.e.e 1098.e 9.c $24$ $8.768$ None 1098.2.e.e \(-12\) \(2\) \(3\) \(11\) $\mathrm{SU}(2)[C_{3}]$
1098.2.e.f 1098.e 9.c $34$ $8.768$ None 1098.2.e.f \(-17\) \(2\) \(-5\) \(-11\) $\mathrm{SU}(2)[C_{3}]$
1098.2.e.g 1098.e 9.c $34$ $8.768$ None 1098.2.e.g \(17\) \(4\) \(5\) \(-13\) $\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1098, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1098, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(549, [\chi])\)\(^{\oplus 2}\)