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Properties

Label 1026.2.e
Level $1026$
Weight $2$
Character orbit 1026.e
Rep. character $\chi_{1026}(343,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $4$
Sturm bound $360$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1026.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 4 \)
Sturm bound: \(360\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1026, [\chi])\).

Total New Old
Modular forms 384 36 348
Cusp forms 336 36 300
Eisenstein series 48 0 48

Trace form

\( 36 q - 18 q^{4} + O(q^{10}) \) \( 36 q - 18 q^{4} + 4 q^{11} + 4 q^{14} - 18 q^{16} + 16 q^{17} + 4 q^{23} - 30 q^{25} + 8 q^{26} - 12 q^{29} - 12 q^{31} - 48 q^{35} + 24 q^{37} - 6 q^{38} - 20 q^{41} - 8 q^{44} + 24 q^{46} + 10 q^{47} - 30 q^{49} + 56 q^{53} + 4 q^{56} + 12 q^{58} + 4 q^{59} - 12 q^{61} + 8 q^{62} + 36 q^{64} + 36 q^{65} - 12 q^{67} - 8 q^{68} - 88 q^{71} - 14 q^{74} + 4 q^{77} - 12 q^{79} - 48 q^{82} - 40 q^{83} + 8 q^{86} - 8 q^{89} + 48 q^{91} + 4 q^{92} - 12 q^{94} + 12 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1026, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1026.2.e.a 1026.e 9.c $6$ $8.193$ \(\Q(\zeta_{18})\) None 342.2.e.b \(-3\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18})q^{2}-\zeta_{18}q^{4}+(-2\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
1026.2.e.b 1026.e 9.c $6$ $8.193$ 6.0.309123.1 None 342.2.e.a \(3\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{4})q^{2}-\beta _{4}q^{4}+(1+\beta _{2}-\beta _{4}+\cdots)q^{7}+\cdots\)
1026.2.e.c 1026.e 9.c $12$ $8.193$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 342.2.e.d \(-6\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{5})q^{2}-\beta _{5}q^{4}+\beta _{10}q^{5}+\cdots\)
1026.2.e.d 1026.e 9.c $12$ $8.193$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 342.2.e.c \(6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{2}+(-1+\beta _{4})q^{4}+\beta _{7}q^{5}+(-\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1026, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1026, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(513, [\chi])\)\(^{\oplus 2}\)