Properties

Label 27.8.a
Level 27
Weight 8
Character orbit a
Rep. character \(\chi_{27}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 5
Sturm bound 24
Trace bound 4

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 27.a (trivial)
Character field: \(\Q\)
Newforms: \( 5 \)
Sturm bound: \(24\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(27))\).

Total New Old
Modular forms 24 9 15
Cusp forms 18 9 9
Eisenstein series 6 0 6

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

\(3\)Dim.
\(+\)\(5\)
\(-\)\(4\)

Trace form

\( 9q + 486q^{4} - 477q^{7} + O(q^{10}) \) \( 9q + 486q^{4} - 477q^{7} + 10566q^{10} + 3465q^{13} - 14166q^{16} - 62379q^{19} + 276930q^{22} - 116289q^{25} - 306054q^{28} + 459468q^{31} - 1531440q^{34} - 293553q^{37} + 3203082q^{40} - 1441656q^{43} - 1755612q^{46} + 4729986q^{49} - 688860q^{52} - 178056q^{55} + 580140q^{58} - 974637q^{61} - 4297662q^{64} - 1320615q^{67} - 8772174q^{70} + 6787089q^{73} - 16525728q^{76} + 30330405q^{79} + 26821620q^{82} - 34065792q^{85} + 11245590q^{88} - 33990489q^{91} - 8233524q^{94} + 20656197q^{97} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(27))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3
27.8.a.a \(1\) \(8.434\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1763\) \(+\) \(q-2^{7}q^{4}+1763q^{7}+12605q^{13}+\cdots\)
27.8.a.b \(2\) \(8.434\) \(\Q(\sqrt{65}) \) None \(-9\) \(0\) \(-180\) \(700\) \(-\) \(q+(-5-\beta )q^{2}+(43+9\beta )q^{4}+(-91+\cdots)q^{5}+\cdots\)
27.8.a.c \(2\) \(8.434\) \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-1118\) \(-\) \(q+\beta q^{2}-20q^{4}-34\beta q^{5}-559q^{7}+\cdots\)
27.8.a.d \(2\) \(8.434\) \(\Q(\sqrt{42}) \) None \(0\) \(0\) \(0\) \(-2522\) \(+\) \(q+\beta q^{2}+250q^{4}+20\beta q^{5}-1261q^{7}+\cdots\)
27.8.a.e \(2\) \(8.434\) \(\Q(\sqrt{65}) \) None \(9\) \(0\) \(180\) \(700\) \(+\) \(q+(5+\beta )q^{2}+(43+9\beta )q^{4}+(91+2\beta )q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(27))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(27)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 2}\)