Properties

Label 23.4.a
Level $23$
Weight $4$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $2$
Sturm bound $8$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(23))\).

Total New Old
Modular forms 7 5 2
Cusp forms 5 5 0
Eisenstein series 2 0 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(23\)Dim
\(+\)\(4\)
\(-\)\(1\)

Trace form

\( 5 q + 2 q^{3} + 16 q^{4} + 8 q^{5} - 7 q^{6} + 8 q^{7} - 39 q^{8} - 35 q^{9} - 58 q^{10} + 42 q^{11} - 47 q^{12} + 54 q^{13} - 128 q^{14} + 40 q^{15} + 48 q^{16} + 18 q^{17} + 53 q^{18} + 26 q^{19} + 164 q^{20}+ \cdots - 1566 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23
23.4.a.a 23.a 1.a $1$ $1.357$ \(\Q\) None 23.4.a.a \(-2\) \(-5\) \(-6\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b 23.a 1.a $4$ $1.357$ 4.4.334189.1 None 23.4.a.b \(2\) \(7\) \(14\) \(16\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)