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Properties

Label 1890.2.m
Level $1890$
Weight $2$
Character orbit 1890.m
Rep. character $\chi_{1890}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $96$
Newform subspaces $4$
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.m (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(864\)
Trace bound: \(5\)

Dimensions

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

Total New Old
Modular forms 912 96 816
Cusp forms 816 96 720
Eisenstein series 96 0 96

Trace form

\( 96 q + O(q^{10}) \) \( 96 q - 48 q^{13} - 96 q^{16} + 8 q^{22} - 8 q^{25} - 16 q^{31} - 40 q^{37} + 32 q^{40} + 16 q^{43} + 16 q^{46} + 48 q^{52} + 16 q^{55} + 32 q^{58} - 48 q^{67} + 8 q^{70} - 32 q^{82} - 24 q^{85} + 8 q^{88} + 64 q^{97} + O(q^{100}) \)

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.m.a 1890.m 15.e $24$ $15.092$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1890.2.m.b 1890.m 15.e $24$ $15.092$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1890.2.m.c 1890.m 15.e $24$ $15.092$ None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
1890.2.m.d 1890.m 15.e $24$ $15.092$ None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(1890, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(270, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(945, [\chi])\)\(^{\oplus 2}\)