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Properties

Label 1890.2.j
Level $1890$
Weight $2$
Character orbit 1890.j
Rep. character $\chi_{1890}(631,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $48$
Newform subspaces $12$
Sturm bound $864$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(864\)
Trace bound: \(11\)
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 48 864
Cusp forms 816 48 768
Eisenstein series 96 0 96

Trace form

\( 48 q + 4 q^{2} - 24 q^{4} - 8 q^{8} + O(q^{10}) \) \( 48 q + 4 q^{2} - 24 q^{4} - 8 q^{8} - 8 q^{11} - 24 q^{16} + 8 q^{17} - 24 q^{19} + 12 q^{22} - 24 q^{25} - 16 q^{29} + 4 q^{32} + 12 q^{34} - 8 q^{35} - 4 q^{38} - 20 q^{41} + 12 q^{43} + 16 q^{44} + 48 q^{47} - 24 q^{49} + 4 q^{50} - 16 q^{53} + 28 q^{59} + 48 q^{62} + 48 q^{64} + 12 q^{65} + 12 q^{67} - 4 q^{68} - 56 q^{71} - 24 q^{73} - 16 q^{74} + 12 q^{76} + 16 q^{77} + 12 q^{79} - 24 q^{82} - 48 q^{83} + 12 q^{85} - 20 q^{86} + 12 q^{88} + 112 q^{89} - 24 q^{91} - 16 q^{95} + 12 q^{97} - 8 q^{98} + O(q^{100}) \)

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.j.a 1890.j 9.c $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.j.b 1890.j 9.c $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.j.c 1890.j 9.c $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.j.d 1890.j 9.c $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.j.e 1890.j 9.c $2$ $15.092$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.j.f 1890.j 9.c $4$ $15.092$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(0\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}-\beta _{1}q^{5}+(1+\cdots)q^{7}+\cdots\)
1890.2.j.g 1890.j 9.c $4$ $15.092$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(1-\beta _{1})q^{5}+\cdots\)
1890.2.j.h 1890.j 9.c $4$ $15.092$ \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{12})q^{2}-\zeta_{12}q^{4}+\zeta_{12}q^{5}+\cdots\)
1890.2.j.i 1890.j 9.c $6$ $15.092$ 6.0.954288.1 None \(3\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
1890.2.j.j 1890.j 9.c $6$ $15.092$ 6.0.954288.1 None \(3\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}+(-1+\beta _{3})q^{4}+(1-\beta _{3})q^{5}+\cdots\)
1890.2.j.k 1890.j 9.c $6$ $15.092$ 6.0.954288.1 None \(3\) \(0\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{2}-\beta _{3}q^{4}+\beta _{3}q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots\)
1890.2.j.l 1890.j 9.c $8$ $15.092$ 8.0.856615824.2 None \(4\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(54, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)