↑

Properties

Label 1890.2.bk
Level $1890$
Weight $2$
Character orbit 1890.bk
Rep. character $\chi_{1890}(341,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $64$
Newform subspaces $3$
Sturm bound $864$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1890.bk (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(864\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(11\)

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

\( 64 q - 64 q^{4} - 4 q^{7} + O(q^{10}) \) \( 64 q - 64 q^{4} - 4 q^{7} + 12 q^{11} - 12 q^{13} - 6 q^{14} + 64 q^{16} - 36 q^{23} - 32 q^{25} + 24 q^{26} + 4 q^{28} + 6 q^{29} + 4 q^{37} - 6 q^{41} + 4 q^{43} - 12 q^{44} - 6 q^{46} - 72 q^{47} + 10 q^{49} + 12 q^{52} - 72 q^{53} + 6 q^{56} + 120 q^{59} - 64 q^{64} + 56 q^{67} + 12 q^{70} + 36 q^{74} + 12 q^{77} - 16 q^{79} + 12 q^{85} + 48 q^{86} + 6 q^{89} + 24 q^{91} + 36 q^{92} - 12 q^{97} - 48 q^{98} + O(q^{100}) \)

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.bk.a 1890.bk 63.i $4$ $15.092$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{12}^{3}q^{2}-q^{4}+\zeta_{12}^{2}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1890.2.bk.b 1890.bk 63.i $28$ $15.092$ None \(0\) \(0\) \(14\) \(8\) $\mathrm{SU}(2)[C_{6}]$
1890.2.bk.c 1890.bk 63.i $32$ $15.092$ None \(0\) \(0\) \(-16\) \(-2\) $\mathrm{SU}(2)[C_{6}]$

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

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