Properties

Label 6021.2.a
Level 6021
Weight 2
Character orbit a
Rep. character \(\chi_{6021}(1,\cdot)\)
Character field \(\Q\)
Dimension 296
Newforms 20
Sturm bound 1344
Trace bound 5

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Defining parameters

Level: \( N \) = \( 6021 = 3^{3} \cdot 223 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6021.a (trivial)
Character field: \(\Q\)
Newforms: \( 20 \)
Sturm bound: \(1344\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6021))\).

Total New Old
Modular forms 678 296 382
Cusp forms 667 296 371
Eisenstein series 11 0 11

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

\(3\)\(223\)FrickeDim.
\(+\)\(+\)\(+\)\(71\)
\(+\)\(-\)\(-\)\(77\)
\(-\)\(+\)\(-\)\(77\)
\(-\)\(-\)\(+\)\(71\)
Plus space\(+\)\(142\)
Minus space\(-\)\(154\)

Trace form

\(296q \) \(\mathstrut +\mathstrut 300q^{4} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(296q \) \(\mathstrut +\mathstrut 300q^{4} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 284q^{16} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut +\mathstrut 280q^{25} \) \(\mathstrut -\mathstrut 32q^{28} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 28q^{34} \) \(\mathstrut -\mathstrut 40q^{37} \) \(\mathstrut -\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 272q^{49} \) \(\mathstrut -\mathstrut 24q^{52} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 32q^{61} \) \(\mathstrut +\mathstrut 288q^{64} \) \(\mathstrut -\mathstrut 48q^{67} \) \(\mathstrut -\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut -\mathstrut 68q^{76} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut -\mathstrut 72q^{82} \) \(\mathstrut -\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 104q^{88} \) \(\mathstrut +\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6021))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 223
6021.2.a.a \(1\) \(48.078\) \(\Q\) None \(-2\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-q^{7}-q^{13}+2q^{14}+\cdots\)
6021.2.a.b \(1\) \(48.078\) \(\Q\) None \(-2\) \(0\) \(3\) \(1\) \(+\) \(+\) \(q-2q^{2}+2q^{4}+3q^{5}+q^{7}-6q^{10}+\cdots\)
6021.2.a.c \(1\) \(48.078\) \(\Q\) None \(-1\) \(0\) \(3\) \(-2\) \(+\) \(+\) \(q-q^{2}-q^{4}+3q^{5}-2q^{7}+3q^{8}-3q^{10}+\cdots\)
6021.2.a.d \(1\) \(48.078\) \(\Q\) None \(0\) \(0\) \(-3\) \(-3\) \(-\) \(+\) \(q-2q^{4}-3q^{5}-3q^{7}+4q^{11}-2q^{13}+\cdots\)
6021.2.a.e \(1\) \(48.078\) \(\Q\) None \(0\) \(0\) \(3\) \(-3\) \(+\) \(+\) \(q-2q^{4}+3q^{5}-3q^{7}-4q^{11}-2q^{13}+\cdots\)
6021.2.a.f \(1\) \(48.078\) \(\Q\) None \(1\) \(0\) \(-3\) \(-2\) \(+\) \(+\) \(q+q^{2}-q^{4}-3q^{5}-2q^{7}-3q^{8}-3q^{10}+\cdots\)
6021.2.a.g \(1\) \(48.078\) \(\Q\) None \(2\) \(0\) \(-3\) \(1\) \(-\) \(+\) \(q+2q^{2}+2q^{4}-3q^{5}+q^{7}-6q^{10}+\cdots\)
6021.2.a.h \(1\) \(48.078\) \(\Q\) None \(2\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(q+2q^{2}+2q^{4}-q^{7}-q^{13}-2q^{14}+\cdots\)
6021.2.a.i \(2\) \(48.078\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(2\) \(-\) \(-\) \(q+\beta q^{2}+(-1+2\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots\)
6021.2.a.j \(2\) \(48.078\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(2\) \(+\) \(-\) \(q+\beta q^{2}+(1+2\beta )q^{5}+q^{7}-2\beta q^{8}+\cdots\)
6021.2.a.k \(4\) \(48.078\) \(\Q(\sqrt{2}, \sqrt{5})\) None \(0\) \(0\) \(0\) \(4\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{5}+q^{7}-2\beta _{2}q^{8}+\cdots\)
6021.2.a.l \(10\) \(48.078\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(2+\beta _{3}+\beta _{6}+\beta _{8})q^{4}+(\beta _{4}+\cdots)q^{5}+\cdots\)
6021.2.a.m \(30\) \(48.078\) None \(0\) \(0\) \(0\) \(-10\) \(+\) \(+\)
6021.2.a.n \(30\) \(48.078\) None \(0\) \(0\) \(0\) \(14\) \(-\) \(+\)
6021.2.a.o \(30\) \(48.078\) None \(0\) \(0\) \(0\) \(-20\) \(-\) \(-\)
6021.2.a.p \(35\) \(48.078\) None \(-4\) \(0\) \(-14\) \(2\) \(+\) \(+\)
6021.2.a.q \(35\) \(48.078\) None \(-4\) \(0\) \(-10\) \(-2\) \(-\) \(-\)
6021.2.a.r \(35\) \(48.078\) None \(4\) \(0\) \(10\) \(-2\) \(+\) \(-\)
6021.2.a.s \(35\) \(48.078\) None \(4\) \(0\) \(14\) \(2\) \(-\) \(+\)
6021.2.a.t \(40\) \(48.078\) None \(0\) \(0\) \(0\) \(16\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6021))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6021)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(669))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2007))\)\(^{\oplus 2}\)