Properties

Label 30.2.a
Level 3030
Weight 22
Character orbit 30.a
Rep. character χ30(1,)\chi_{30}(1,\cdot)
Character field Q\Q
Dimension 11
Newform subspaces 11
Sturm bound 1212
Trace bound 00

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Defining parameters

Level: N N == 30=235 30 = 2 \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 30.a (trivial)
Character field: Q\Q
Newform subspaces: 1 1
Sturm bound: 1212
Trace bound: 00

Dimensions

The following table gives the dimensions of various subspaces of M2(Γ0(30))M_{2}(\Gamma_0(30)).

Total New Old
Modular forms 10 1 9
Cusp forms 3 1 2
Eisenstein series 7 0 7

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

223355FrickeTotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++++--220022110011110011
++-++-221111111100110011
++--++110011000000110011
-++++-110011000000110011
-++-++220022110011110011
--++++110011000000110011
----110011000000110011
Plus space++440044110011330033
Minus space-661155221111440044

Trace form

qq2+q3+q4q5q64q7q8+q9+q10+q12+2q13+4q14q15+q16+6q17q184q19q204q21q24+q25+9q98+O(q100) q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} + q^{12} + 2 q^{13} + 4 q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} - 4 q^{19} - q^{20} - 4 q^{21} - q^{24} + q^{25}+ \cdots - 9 q^{98}+O(q^{100}) Copy content Toggle raw display

Decomposition of S2new(Γ0(30))S_{2}^{\mathrm{new}}(\Gamma_0(30)) 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} 2 3 5
30.2.a.a 30.a 1.a 11 0.2400.240 Q\Q None 30.2.a.a 1-1 11 1-1 4-4 ++ - ++ SU(2)\mathrm{SU}(2) qq2+q3+q4q5q64q7+q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-4q^{7}+\cdots

Decomposition of S2old(Γ0(30))S_{2}^{\mathrm{old}}(\Gamma_0(30)) into lower level spaces

S2old(Γ0(30)) S_{2}^{\mathrm{old}}(\Gamma_0(30)) \simeq S2new(Γ0(15))S_{2}^{\mathrm{new}}(\Gamma_0(15))2^{\oplus 2}