Properties

Label 8001.2.a
Level 8001
Weight 2
Character orbit a
Rep. character \(\chi_{8001}(1,\cdot)\)
Character field \(\Q\)
Dimension 314
Newforms 27
Sturm bound 2048
Trace bound 5

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Defining parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)
Character field: \(\Q\)
Newforms: \( 27 \)
Sturm bound: \(2048\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8001))\).

Total New Old
Modular forms 1032 314 718
Cusp forms 1017 314 703
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.

\(3\)\(7\)\(127\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(32\)
\(+\)\(+\)\(-\)\(-\)\(30\)
\(+\)\(-\)\(+\)\(-\)\(40\)
\(+\)\(-\)\(-\)\(+\)\(22\)
\(-\)\(+\)\(+\)\(-\)\(47\)
\(-\)\(+\)\(-\)\(+\)\(48\)
\(-\)\(-\)\(+\)\(+\)\(43\)
\(-\)\(-\)\(-\)\(-\)\(52\)
Plus space\(+\)\(145\)
Minus space\(-\)\(169\)

Trace form

\( 314q + 320q^{4} - 4q^{5} + O(q^{10}) \) \( 314q + 320q^{4} - 4q^{5} + 4q^{10} + 16q^{11} - 8q^{13} + 332q^{16} - 4q^{17} + 4q^{19} + 4q^{20} - 28q^{22} - 4q^{23} + 290q^{25} - 40q^{26} + 12q^{31} - 30q^{32} - 26q^{34} + 8q^{35} - 16q^{37} + 6q^{38} - 32q^{40} - 8q^{41} - 8q^{43} + 38q^{44} + 16q^{46} + 36q^{47} + 314q^{49} + 32q^{50} - 30q^{52} + 16q^{53} - 8q^{55} + 20q^{58} + 20q^{59} + 12q^{61} - 62q^{62} + 332q^{64} - 36q^{65} - 8q^{67} + 72q^{68} + 28q^{70} + 52q^{71} - 64q^{73} - 38q^{74} - 24q^{76} + 16q^{79} - 20q^{80} - 24q^{82} + 16q^{83} + 28q^{85} + 24q^{86} - 10q^{88} - 32q^{89} - 4q^{91} - 52q^{92} + 40q^{94} - 44q^{95} - 108q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8001))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 7 127
8001.2.a.a \(1\) \(63.888\) \(\Q\) None \(-2\) \(0\) \(-3\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{2}+2q^{4}-3q^{5}-q^{7}+6q^{10}+\cdots\)
8001.2.a.b \(1\) \(63.888\) \(\Q\) None \(-2\) \(0\) \(-1\) \(-1\) \(+\) \(+\) \(-\) \(q-2q^{2}+2q^{4}-q^{5}-q^{7}+2q^{10}+\cdots\)
8001.2.a.c \(1\) \(63.888\) \(\Q\) None \(0\) \(0\) \(-3\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{4}-3q^{5}+q^{7}-6q^{11}-q^{13}+\cdots\)
8001.2.a.d \(1\) \(63.888\) \(\Q\) None \(1\) \(0\) \(-4\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{2}-q^{4}-4q^{5}-q^{7}-3q^{8}-4q^{10}+\cdots\)
8001.2.a.e \(1\) \(63.888\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+q^{2}-q^{4}+q^{7}-3q^{8}+2q^{13}+q^{14}+\cdots\)
8001.2.a.f \(1\) \(63.888\) \(\Q\) None \(2\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q+2q^{2}+2q^{4}-q^{7}+2q^{13}-2q^{14}+\cdots\)
8001.2.a.g \(1\) \(63.888\) \(\Q\) None \(2\) \(0\) \(1\) \(-1\) \(+\) \(+\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}-q^{7}+2q^{10}+\cdots\)
8001.2.a.h \(2\) \(63.888\) \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(-3\) \(-2\) \(-\) \(+\) \(-\) \(q-\beta q^{2}+(2+\beta )q^{4}+(-1-\beta )q^{5}-q^{7}+\cdots\)
8001.2.a.i \(2\) \(63.888\) \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-2\) \(-\) \(+\) \(-\) \(q-2q^{4}+(1+\beta )q^{5}-q^{7}+(2-2\beta )q^{11}+\cdots\)
8001.2.a.j \(2\) \(63.888\) \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{2}-\beta q^{5}+q^{7}-2\beta q^{8}-2q^{10}+\cdots\)
8001.2.a.k \(2\) \(63.888\) \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+4q^{4}+\beta q^{5}+q^{7}+2\beta q^{8}+\cdots\)
8001.2.a.l \(7\) \(63.888\) 7.7.118870813.1 None \(2\) \(0\) \(8\) \(7\) \(-\) \(-\) \(+\) \(q-\beta _{4}q^{2}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
8001.2.a.m \(11\) \(63.888\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(2\) \(0\) \(-1\) \(-11\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{7}q^{5}-q^{7}+\cdots\)
8001.2.a.n \(12\) \(63.888\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(7\) \(0\) \(7\) \(12\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
8001.2.a.o \(13\) \(63.888\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(0\) \(-12\) \(13\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{10}+\cdots)q^{5}+\cdots\)
8001.2.a.p \(14\) \(63.888\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(5\) \(0\) \(4\) \(-14\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}-q^{7}+\cdots\)
8001.2.a.q \(15\) \(63.888\) \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(0\) \(0\) \(-7\) \(-15\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}-q^{7}+\cdots\)
8001.2.a.r \(16\) \(63.888\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-5\) \(0\) \(1\) \(-16\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{13}q^{5}-q^{7}+\cdots\)
8001.2.a.s \(16\) \(63.888\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-4\) \(0\) \(-5\) \(-16\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{7}q^{5}-q^{7}+\cdots\)
8001.2.a.t \(16\) \(63.888\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(2\) \(0\) \(9\) \(-16\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{11})q^{5}+\cdots\)
8001.2.a.u \(18\) \(63.888\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(6\) \(0\) \(10\) \(18\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{12})q^{5}+\cdots\)
8001.2.a.v \(19\) \(63.888\) \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(-4\) \(0\) \(-5\) \(19\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{10}q^{5}+q^{7}+\cdots\)
8001.2.a.w \(20\) \(63.888\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-8\) \(0\) \(-3\) \(20\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{16}q^{5}+q^{7}+\cdots\)
8001.2.a.x \(22\) \(63.888\) None \(0\) \(0\) \(0\) \(22\) \(+\) \(-\) \(-\)
8001.2.a.y \(28\) \(63.888\) None \(0\) \(0\) \(0\) \(-28\) \(+\) \(+\) \(-\)
8001.2.a.z \(32\) \(63.888\) None \(0\) \(0\) \(0\) \(-32\) \(+\) \(+\) \(+\)
8001.2.a.ba \(40\) \(63.888\) None \(0\) \(0\) \(0\) \(40\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8001))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8001)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(127))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(381))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(889))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1143))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2667))\)\(^{\oplus 2}\)