Properties

Label 5.34.a
Level 55
Weight 3434
Character orbit 5.a
Rep. character χ5(1,)\chi_{5}(1,\cdot)
Character field Q\Q
Dimension 1111
Newform subspaces 22
Sturm bound 1717
Trace bound 11

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Defining parameters

Level: N N == 5 5
Weight: k k == 34 34
Character orbit: [χ][\chi] == 5.a (trivial)
Character field: Q\Q
Newform subspaces: 2 2
Sturm bound: 1717
Trace bound: 11
Distinguishing TpT_p: 22

Dimensions

The following table gives the dimensions of various subspaces of M34(Γ0(5))M_{34}(\Gamma_0(5)).

Total New Old
Modular forms 17 11 6
Cusp forms 15 11 4
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.

55TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
++885533775522110011
-996633886622110011

Trace form

11q+177822q2+11525186q3+30661957012q4+152587890625q5+19540822365112q646338728939658q7+32 ⁣ ⁣00q8+28 ⁣ ⁣03q9+17 ⁣ ⁣50q1013 ⁣ ⁣48q11+12 ⁣ ⁣04q99+O(q100) 11 q + 177822 q^{2} + 11525186 q^{3} + 30661957012 q^{4} + 152587890625 q^{5} + 19540822365112 q^{6} - 46338728939658 q^{7} + 32\!\cdots\!00 q^{8} + 28\!\cdots\!03 q^{9} + 17\!\cdots\!50 q^{10} - 13\!\cdots\!48 q^{11}+ \cdots - 12\!\cdots\!04 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S34new(Γ0(5))S_{34}^{\mathrm{new}}(\Gamma_0(5)) 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} 5
5.34.a.a 5.a 1.a 55 34.49134.491 Q[x]/(x5)\mathbb{Q}[x]/(x^{5} - \cdots) None 5.34.a.a 3047230472 14988714-14988714 762939453125-762939453125 65 ⁣ ⁣58-65\!\cdots\!58 ++ SU(2)\mathrm{SU}(2) q+(6094β1)q2+(2997861296β1+)q3+q+(6094-\beta _{1})q^{2}+(-2997861-296\beta _{1}+\cdots)q^{3}+\cdots
5.34.a.b 5.a 1.a 66 34.49134.491 Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots) None 5.34.a.b 147350147350 2651390026513900 915527343750915527343750 19 ⁣ ⁣0019\!\cdots\!00 - SU(2)\mathrm{SU}(2) q+(24558+β1)q2+(4418958+77β1+)q3+q+(24558+\beta _{1})q^{2}+(4418958+77\beta _{1}+\cdots)q^{3}+\cdots

Decomposition of S34old(Γ0(5))S_{34}^{\mathrm{old}}(\Gamma_0(5)) into lower level spaces

S34old(Γ0(5)) S_{34}^{\mathrm{old}}(\Gamma_0(5)) \simeq S34new(Γ0(1))S_{34}^{\mathrm{new}}(\Gamma_0(1))2^{\oplus 2}