Properties

Label 42.6.a
Level 4242
Weight 66
Character orbit 42.a
Rep. character χ42(1,)\chi_{42}(1,\cdot)
Character field Q\Q
Dimension 66
Newform subspaces 66
Sturm bound 4848
Trace bound 55

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Defining parameters

Level: N N == 42=237 42 = 2 \cdot 3 \cdot 7
Weight: k k == 6 6
Character orbit: [χ][\chi] == 42.a (trivial)
Character field: Q\Q
Newform subspaces: 6 6
Sturm bound: 4848
Trace bound: 55
Distinguishing TpT_p: 55

Dimensions

The following table gives the dimensions of various subspaces of M6(Γ0(42))M_{6}(\Gamma_0(42)).

Total New Old
Modular forms 44 6 38
Cusp forms 36 6 30
Eisenstein series 8 0 8

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

223377FrickeDim
++++++++11
++++--11
++-++-11
++--++11
-++++-11
----11
Plus space++22
Minus space-44

Trace form

6q8q2+96q4+44q5128q8+486q9+624q10+712q1136q13792q15+1536q16+1468q17648q184080q19+704q20+882q21+2880q22++57672q99+O(q100) 6 q - 8 q^{2} + 96 q^{4} + 44 q^{5} - 128 q^{8} + 486 q^{9} + 624 q^{10} + 712 q^{11} - 36 q^{13} - 792 q^{15} + 1536 q^{16} + 1468 q^{17} - 648 q^{18} - 4080 q^{19} + 704 q^{20} + 882 q^{21} + 2880 q^{22}+ \cdots + 57672 q^{99}+O(q^{100}) Copy content Toggle raw display

Decomposition of S6new(Γ0(42))S_{6}^{\mathrm{new}}(\Gamma_0(42)) 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 7
42.6.a.a 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.a 4-4 9-9 54-54 4949 ++ ++ - SU(2)\mathrm{SU}(2) q4q29q3+24q454q5+62q6+q-4q^{2}-9q^{3}+2^{4}q^{4}-54q^{5}+6^{2}q^{6}+\cdots
42.6.a.b 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.b 4-4 9-9 4444 49-49 ++ ++ ++ SU(2)\mathrm{SU}(2) q4q29q3+24q4+44q5+62q6+q-4q^{2}-9q^{3}+2^{4}q^{4}+44q^{5}+6^{2}q^{6}+\cdots
42.6.a.c 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.c 4-4 99 72-72 4949 ++ - - SU(2)\mathrm{SU}(2) q4q2+9q3+24q472q562q6+q-4q^{2}+9q^{3}+2^{4}q^{4}-72q^{5}-6^{2}q^{6}+\cdots
42.6.a.d 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.d 4-4 99 2626 49-49 ++ - ++ SU(2)\mathrm{SU}(2) q4q2+9q3+24q4+26q562q6+q-4q^{2}+9q^{3}+2^{4}q^{4}+26q^{5}-6^{2}q^{6}+\cdots
42.6.a.e 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.e 44 9-9 7676 49-49 - ++ ++ SU(2)\mathrm{SU}(2) q+4q29q3+24q4+76q562q6+q+4q^{2}-9q^{3}+2^{4}q^{4}+76q^{5}-6^{2}q^{6}+\cdots
42.6.a.f 42.a 1.a 11 6.7366.736 Q\Q None 42.6.a.f 44 99 2424 4949 - - - SU(2)\mathrm{SU}(2) q+4q2+9q3+24q4+24q5+62q6+q+4q^{2}+9q^{3}+2^{4}q^{4}+24q^{5}+6^{2}q^{6}+\cdots

Decomposition of S6old(Γ0(42))S_{6}^{\mathrm{old}}(\Gamma_0(42)) into lower level spaces

S6old(Γ0(42)) S_{6}^{\mathrm{old}}(\Gamma_0(42)) \simeq S6new(Γ0(3))S_{6}^{\mathrm{new}}(\Gamma_0(3))4^{\oplus 4}\oplusS6new(Γ0(6))S_{6}^{\mathrm{new}}(\Gamma_0(6))2^{\oplus 2}\oplusS6new(Γ0(7))S_{6}^{\mathrm{new}}(\Gamma_0(7))4^{\oplus 4}\oplusS6new(Γ0(14))S_{6}^{\mathrm{new}}(\Gamma_0(14))2^{\oplus 2}\oplusS6new(Γ0(21))S_{6}^{\mathrm{new}}(\Gamma_0(21))2^{\oplus 2}