↑

Properties

Label 1197.2.f
Level $1197$
Weight $2$
Character orbit 1197.f
Rep. character $\chi_{1197}(512,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $3$
Sturm bound $320$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1197 = 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1197.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 57 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(320\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1197, [\chi])\).

Total New Old
Modular forms 168 40 128
Cusp forms 152 40 112
Eisenstein series 16 0 16

Trace form

\( 40 q + 56 q^{4} + O(q^{10}) \) \( 40 q + 56 q^{4} + 56 q^{16} + 8 q^{19} - 40 q^{25} + 16 q^{43} + 40 q^{49} + 48 q^{55} - 112 q^{61} + 136 q^{64} - 16 q^{73} - 8 q^{76} + 64 q^{82} + 48 q^{85} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1197, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1197.2.f.a 1197.f 57.d $4$ $9.558$ \(\Q(\sqrt{-2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+3q^{4}+2\beta _{1}q^{5}-q^{7}+\beta _{3}q^{8}+\cdots\)
1197.2.f.b 1197.f 57.d $16$ $9.558$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}+(\beta _{1}+\beta _{5})q^{4}+\beta _{9}q^{5}-q^{7}+\cdots\)
1197.2.f.c 1197.f 57.d $20$ $9.558$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{2}+(1-\beta _{1})q^{4}-\beta _{18}q^{5}+q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1197, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1197, [\chi]) \cong \)