Properties

Label 2.72.a
Level 22
Weight 7272
Character orbit 2.a
Rep. character χ2(1,)\chi_{2}(1,\cdot)
Character field Q\Q
Dimension 55
Newform subspaces 22
Sturm bound 1818
Trace bound 11

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Defining parameters

Level: N N == 2 2
Weight: k k == 72 72
Character orbit: [χ][\chi] == 2.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 1818
Trace bound: 11
Distinguishing TpT_p: 33

Dimensions

The following table gives the dimensions of various subspaces of M72(Γ0(2))M_{72}(\Gamma_0(2)).

Total New Old
Modular forms 19 5 14
Cusp forms 17 5 12
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.

22TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++10103377993366110011
-992277882266110011

Trace form

5q34359738368q270 ⁣ ⁣88q3+59 ⁣ ⁣20q4+87 ⁣ ⁣50q525 ⁣ ⁣80q697 ⁣ ⁣24q740 ⁣ ⁣32q810 ⁣ ⁣15q925 ⁣ ⁣00q10++12 ⁣ ⁣20q99+O(q100) 5 q - 34359738368 q^{2} - 70\!\cdots\!88 q^{3} + 59\!\cdots\!20 q^{4} + 87\!\cdots\!50 q^{5} - 25\!\cdots\!80 q^{6} - 97\!\cdots\!24 q^{7} - 40\!\cdots\!32 q^{8} - 10\!\cdots\!15 q^{9} - 25\!\cdots\!00 q^{10}+ \cdots + 12\!\cdots\!20 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S72new(Γ0(2))S_{72}^{\mathrm{new}}(\Gamma_0(2)) 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
2.72.a.a 2.a 1.a 22 63.84963.849 Q[x]/(x2)\mathbb{Q}[x]/(x^{2} - \cdots) None 2.72.a.a 6871947673668719476736 73 ⁣ ⁣24-73\!\cdots\!24 40 ⁣ ⁣0040\!\cdots\!00 29 ⁣ ⁣52-29\!\cdots\!52 - SU(2)\mathrm{SU}(2) q+235q2+(36645276287423412+)q3+q+2^{35}q^{2}+(-36645276287423412+\cdots)q^{3}+\cdots
2.72.a.b 2.a 1.a 33 63.84963.849 Q[x]/(x3)\mathbb{Q}[x]/(x^{3} - \cdots) None 2.72.a.b 103079215104-103079215104 23 ⁣ ⁣3623\!\cdots\!36 47 ⁣ ⁣5047\!\cdots\!50 68 ⁣ ⁣72-68\!\cdots\!72 ++ SU(2)\mathrm{SU}(2) q235q2+(787523430902412+β1+)q3+q-2^{35}q^{2}+(787523430902412+\beta _{1}+\cdots)q^{3}+\cdots

Decomposition of S72old(Γ0(2))S_{72}^{\mathrm{old}}(\Gamma_0(2)) into lower level spaces

S72old(Γ0(2)) S_{72}^{\mathrm{old}}(\Gamma_0(2)) \simeq S72new(Γ0(1))S_{72}^{\mathrm{new}}(\Gamma_0(1))2^{\oplus 2}