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Properties

Label 1890.2.l
Level $1890$
Weight $2$
Character orbit 1890.l
Rep. character $\chi_{1890}(361,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $64$
Newform subspaces $9$
Sturm bound $864$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 9 \)
Sturm bound: \(864\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1890, [\chi])\).

Total New Old
Modular forms 912 64 848
Cusp forms 816 64 752
Eisenstein series 96 0 96

Trace form

\( 64 q - 32 q^{4} + 8 q^{5} + 4 q^{7} + O(q^{10}) \) \( 64 q - 32 q^{4} + 8 q^{5} + 4 q^{7} - 8 q^{11} - 4 q^{13} + 2 q^{14} - 32 q^{16} - 16 q^{17} + 8 q^{19} - 4 q^{20} + 24 q^{23} + 64 q^{25} - 8 q^{26} + 4 q^{28} - 10 q^{29} - 4 q^{31} - 4 q^{37} + 48 q^{38} + 22 q^{41} - 4 q^{43} + 4 q^{44} + 6 q^{46} - 12 q^{47} + 16 q^{49} + 8 q^{52} + 8 q^{53} - 4 q^{56} - 20 q^{59} - 22 q^{61} + 64 q^{62} + 64 q^{64} + 4 q^{65} - 28 q^{67} + 32 q^{68} - 6 q^{70} + 88 q^{71} + 56 q^{73} + 24 q^{74} + 8 q^{76} - 20 q^{77} - 16 q^{79} - 4 q^{80} - 24 q^{83} - 12 q^{85} - 40 q^{86} - 2 q^{89} + 32 q^{91} - 12 q^{92} - 12 q^{94} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1890, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1890.2.l.a 1890.l 63.g $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+(2+\zeta_{6})q^{7}+\cdots\)
1890.2.l.b 1890.l 63.g $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
1890.2.l.c 1890.l 63.g $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}+(2-3\zeta_{6})q^{7}+\cdots\)
1890.2.l.d 1890.l 63.g $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+q^{5}+(3-\zeta_{6})q^{7}+\cdots\)
1890.2.l.e 1890.l 63.g $4$ $15.092$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1})q^{2}+\beta _{1}q^{4}+q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
1890.2.l.f 1890.l 63.g $12$ $15.092$ 12.0.\(\cdots\).1 None \(-6\) \(0\) \(-12\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{3})q^{2}+\beta _{3}q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.l.g 1890.l 63.g $12$ $15.092$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{2}+(-1+\beta _{7})q^{4}-q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
1890.2.l.h 1890.l 63.g $12$ $15.092$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}+q^{5}+(-1-\beta _{3}+\cdots)q^{7}+\cdots\)
1890.2.l.i 1890.l 63.g $16$ $15.092$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-8\) \(0\) \(16\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+\beta _{4}q^{4}+q^{5}+\beta _{7}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1890, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)