Properties

Label 6003.2.a
Level 6003
Weight 2
Character orbit a
Rep. character \(\chi_{6003}(1,\cdot)\)
Character field \(\Q\)
Dimension 258
Newforms 23
Sturm bound 1440
Trace bound 5

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Defining parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)
Character field: \(\Q\)
Newforms: \( 23 \)
Sturm bound: \(1440\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6003))\).

Total New Old
Modular forms 728 258 470
Cusp forms 713 258 455
Eisenstein series 15 0 15

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

\(3\)\(23\)\(29\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(22\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(30\)
\(+\)\(-\)\(-\)\(+\)\(22\)
\(-\)\(+\)\(+\)\(-\)\(39\)
\(-\)\(+\)\(-\)\(+\)\(38\)
\(-\)\(-\)\(+\)\(+\)\(35\)
\(-\)\(-\)\(-\)\(-\)\(42\)
Plus space\(+\)\(117\)
Minus space\(-\)\(141\)

Trace form

\(258q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 262q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(258q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 262q^{4} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 270q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 28q^{20} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut +\mathstrut 266q^{25} \) \(\mathstrut +\mathstrut 28q^{26} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut -\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 30q^{32} \) \(\mathstrut -\mathstrut 36q^{34} \) \(\mathstrut +\mathstrut 20q^{35} \) \(\mathstrut +\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 16q^{38} \) \(\mathstrut +\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 40q^{41} \) \(\mathstrut +\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 8q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 302q^{49} \) \(\mathstrut +\mathstrut 66q^{50} \) \(\mathstrut +\mathstrut 32q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 20q^{59} \) \(\mathstrut +\mathstrut 4q^{61} \) \(\mathstrut -\mathstrut 8q^{62} \) \(\mathstrut +\mathstrut 286q^{64} \) \(\mathstrut -\mathstrut 16q^{65} \) \(\mathstrut -\mathstrut 56q^{67} \) \(\mathstrut +\mathstrut 4q^{68} \) \(\mathstrut -\mathstrut 64q^{70} \) \(\mathstrut -\mathstrut 76q^{71} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut -\mathstrut 44q^{74} \) \(\mathstrut -\mathstrut 8q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 16q^{79} \) \(\mathstrut -\mathstrut 4q^{80} \) \(\mathstrut -\mathstrut 32q^{82} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 76q^{88} \) \(\mathstrut -\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 32q^{91} \) \(\mathstrut -\mathstrut 24q^{94} \) \(\mathstrut -\mathstrut 56q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut -\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 23 29
6003.2.a.a \(1\) \(47.934\) \(\Q\) None \(0\) \(0\) \(-4\) \(-4\) \(-\) \(+\) \(-\) \(q-2q^{4}-4q^{5}-4q^{7}-4q^{11}-5q^{13}+\cdots\)
6003.2.a.b \(1\) \(47.934\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-2q^{4}+4q^{11}+3q^{13}+4q^{16}-3q^{17}+\cdots\)
6003.2.a.c \(1\) \(47.934\) \(\Q\) None \(1\) \(0\) \(-3\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}-3q^{5}-3q^{8}-3q^{10}+\cdots\)
6003.2.a.d \(2\) \(47.934\) \(\Q(\sqrt{17}) \) None \(-2\) \(0\) \(3\) \(0\) \(-\) \(+\) \(-\) \(q-q^{2}-q^{4}+(1+\beta )q^{5}+3q^{8}+(-1+\cdots)q^{10}+\cdots\)
6003.2.a.e \(2\) \(47.934\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(-\) \(+\) \(q-2q^{4}+\beta q^{5}+(-2+\beta )q^{7}+q^{13}+\cdots\)
6003.2.a.f \(2\) \(47.934\) \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(4\) \(0\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}+2q^{5}-3q^{8}+2q^{10}+\cdots\)
6003.2.a.g \(4\) \(47.934\) 4.4.5744.1 None \(0\) \(0\) \(2\) \(-2\) \(-\) \(+\) \(+\) \(q-2q^{4}+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+\cdots\)
6003.2.a.h \(5\) \(47.934\) 5.5.312617.1 None \(2\) \(0\) \(3\) \(-5\) \(-\) \(+\) \(+\) \(q+\beta _{3}q^{2}+(2-\beta _{1})q^{4}+(1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
6003.2.a.i \(7\) \(47.934\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(0\) \(5\) \(-5\) \(-\) \(-\) \(+\) \(q+\beta _{3}q^{2}+(1+\beta _{4}+\beta _{5})q^{4}+(1-\beta _{3}+\cdots)q^{5}+\cdots\)
6003.2.a.j \(7\) \(47.934\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(0\) \(3\) \(-5\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
6003.2.a.k \(10\) \(47.934\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(0\) \(-6\) \(3\) \(-\) \(-\) \(+\) \(q-\beta _{3}q^{2}+(2+\beta _{6})q^{4}+(-1-\beta _{4})q^{5}+\cdots\)
6003.2.a.l \(10\) \(47.934\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(0\) \(10\) \(1\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{7})q^{5}+\cdots\)
6003.2.a.m \(11\) \(47.934\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-2\) \(0\) \(-2\) \(3\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
6003.2.a.n \(12\) \(47.934\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(16\) \(-7\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1-\beta _{4}-\beta _{6}+\beta _{8})q^{4}+(1+\cdots)q^{5}+\cdots\)
6003.2.a.o \(13\) \(47.934\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(0\) \(-16\) \(1\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{8})q^{5}+\cdots\)
6003.2.a.p \(14\) \(47.934\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(0\) \(3\) \(-3\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{11}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
6003.2.a.q \(16\) \(47.934\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(0\) \(-16\) \(1\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots\)
6003.2.a.r \(16\) \(47.934\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(1\) \(0\) \(-3\) \(13\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{8}q^{5}+(1-\beta _{10}+\cdots)q^{7}+\cdots\)
6003.2.a.s \(20\) \(47.934\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-2\) \(0\) \(1\) \(9\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{6}q^{5}-\beta _{14}q^{7}+\cdots\)
6003.2.a.t \(22\) \(47.934\) None \(-3\) \(0\) \(0\) \(-6\) \(+\) \(-\) \(-\)
6003.2.a.u \(22\) \(47.934\) None \(3\) \(0\) \(0\) \(-6\) \(+\) \(+\) \(+\)
6003.2.a.v \(30\) \(47.934\) None \(-1\) \(0\) \(0\) \(10\) \(+\) \(-\) \(+\)
6003.2.a.w \(30\) \(47.934\) None \(1\) \(0\) \(0\) \(10\) \(+\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6003))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(6003)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(261))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 2}\)