Properties

Label 23.4.a
Level 2323
Weight 44
Character orbit 23.a
Rep. character χ23(1,)\chi_{23}(1,\cdot)
Character field Q\Q
Dimension 55
Newform subspaces 22
Sturm bound 88
Trace bound 11

Related objects

Downloads

Learn more

Defining parameters

Level: N N == 23 23
Weight: k k == 4 4
Character orbit: [χ][\chi] == 23.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 88
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M4(Γ0(23))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.

2323Dim
++44
-11

Trace form

5q+2q3+16q4+8q57q6+8q739q835q958q10+42q1147q12+54q13128q14+40q15+48q16+18q17+53q18+26q19+164q20+1566q99+O(q100) 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 S4new(Γ0(23))S_{4}^{\mathrm{new}}(\Gamma_0(23)) into newform subspaces

Label Char Prim Dim AA Field CM Minimal twist Traces A-L signs Sato-Tate qq-expansion
a2a_{2} a3a_{3} a5a_{5} a7a_{7} 23
23.4.a.a 23.a 1.a 11 1.3571.357 Q\Q None 23.4.a.a 2-2 5-5 6-6 8-8 - SU(2)\mathrm{SU}(2) q2q25q34q46q5+10q6+q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots
23.4.a.b 23.a 1.a 44 1.3571.357 4.4.334189.1 None 23.4.a.b 22 77 1414 1616 ++ SU(2)\mathrm{SU}(2) q+(1+β3)q2+(1+β1+β2)q3+(6+)q4+q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots