Properties

Label 1890.2.b
Level $1890$
Weight $2$
Character orbit 1890.b
Rep. character $\chi_{1890}(1511,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $4$
Sturm bound $864$
Trace bound $5$

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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(864\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(11\), \(17\), \(41\)

Dimensions

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

Total New Old
Modular forms 456 40 416
Cusp forms 408 40 368
Eisenstein series 48 0 48

Trace form

\( 40 q - 40 q^{4} - 8 q^{7} + O(q^{10}) \) \( 40 q - 40 q^{4} - 8 q^{7} + 40 q^{16} + 40 q^{25} + 8 q^{28} - 16 q^{37} - 8 q^{43} + 8 q^{46} + 8 q^{49} + 8 q^{58} - 40 q^{64} - 8 q^{67} + 16 q^{79} + 40 q^{91} + O(q^{100}) \)

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.b.a 1890.b 21.c $8$ $15.092$ 8.0.303595776.1 None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-q^{4}-q^{5}+(\beta _{1}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
1890.2.b.b 1890.b 21.c $8$ $15.092$ 8.0.303595776.1 None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-q^{4}+q^{5}+(-\beta _{1}+\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\)
1890.2.b.c 1890.b 21.c $12$ $15.092$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-12\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-q^{4}-q^{5}-\beta _{4}q^{7}+\beta _{5}q^{8}+\cdots\)
1890.2.b.d 1890.b 21.c $12$ $15.092$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}-q^{4}+q^{5}+\beta _{6}q^{7}+\beta _{5}q^{8}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)