Properties

Label 1170.2.bj
Level $1170$
Weight $2$
Character orbit 1170.bj
Rep. character $\chi_{1170}(199,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $6$
Sturm bound $504$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bj (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 6 \)
Sturm bound: \(504\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

Total New Old
Modular forms 536 72 464
Cusp forms 472 72 400
Eisenstein series 64 0 64

Trace form

\( 72 q - 36 q^{4} + O(q^{10}) \) \( 72 q - 36 q^{4} - q^{10} - 6 q^{11} + 12 q^{14} - 36 q^{16} - 30 q^{19} - 3 q^{20} - 2 q^{25} + 2 q^{26} - 22 q^{29} + 14 q^{35} + 2 q^{40} - 6 q^{41} - 12 q^{46} - 26 q^{49} + 27 q^{50} + 16 q^{55} - 6 q^{56} + 12 q^{59} - 22 q^{61} + 72 q^{64} + 23 q^{65} + 24 q^{71} - 16 q^{74} + 30 q^{76} + 56 q^{79} + 3 q^{80} - 33 q^{85} + 42 q^{89} - 50 q^{91} + 26 q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1170.2.bj.a $8$ $9.342$ 8.0.\(\cdots\).1 None \(-4\) \(0\) \(3\) \(-5\) \(q+(-1+\beta _{3})q^{2}-\beta _{3}q^{4}+\beta _{6}q^{5}+(-\beta _{3}+\cdots)q^{7}+\cdots\)
1170.2.bj.b $8$ $9.342$ 8.0.\(\cdots\).1 None \(4\) \(0\) \(-3\) \(5\) \(q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}-\beta _{6}q^{5}+(2+\cdots)q^{7}+\cdots\)
1170.2.bj.c $12$ $9.342$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(-2\) \(2\) \(q+(-1-\beta _{4})q^{2}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1170.2.bj.d $12$ $9.342$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(2\) \(-2\) \(q+(1+\beta _{4})q^{2}+\beta _{4}q^{4}+(-\beta _{7}+\beta _{8}+\cdots)q^{5}+\cdots\)
1170.2.bj.e $16$ $9.342$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-8\) \(0\) \(0\) \(0\) \(q+\beta _{7}q^{2}+(-1-\beta _{7})q^{4}-\beta _{2}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)
1170.2.bj.f $16$ $9.342$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(8\) \(0\) \(0\) \(0\) \(q-\beta _{7}q^{2}+(-1-\beta _{7})q^{4}+\beta _{2}q^{5}+(\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)