Properties

Label 8037.2.a
Level 8037
Weight 2
Character orbit a
Rep. character \(\chi_{8037}(1,\cdot)\)
Character field \(\Q\)
Dimension 344
Newforms 24
Sturm bound 1920
Trace bound 7

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Defining parameters

Level: \( N \) = \( 8037 = 3^{2} \cdot 19 \cdot 47 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8037.a (trivial)
Character field: \(\Q\)
Newforms: \( 24 \)
Sturm bound: \(1920\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8037))\).

Total New Old
Modular forms 968 344 624
Cusp forms 953 344 609
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.

\(3\)\(19\)\(47\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(34\)
\(+\)\(+\)\(-\)\(-\)\(34\)
\(+\)\(-\)\(+\)\(-\)\(34\)
\(+\)\(-\)\(-\)\(+\)\(34\)
\(-\)\(+\)\(+\)\(-\)\(53\)
\(-\)\(+\)\(-\)\(+\)\(51\)
\(-\)\(-\)\(+\)\(+\)\(46\)
\(-\)\(-\)\(-\)\(-\)\(58\)
Plus space\(+\)\(165\)
Minus space\(-\)\(179\)

Trace form

\(344q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 338q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(344q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 338q^{4} \) \(\mathstrut -\mathstrut 8q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut -\mathstrut 8q^{11} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut -\mathstrut 10q^{14} \) \(\mathstrut +\mathstrut 310q^{16} \) \(\mathstrut -\mathstrut 8q^{17} \) \(\mathstrut -\mathstrut 36q^{20} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 348q^{25} \) \(\mathstrut +\mathstrut 4q^{26} \) \(\mathstrut +\mathstrut 44q^{28} \) \(\mathstrut -\mathstrut 40q^{29} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut +\mathstrut 12q^{35} \) \(\mathstrut -\mathstrut 24q^{37} \) \(\mathstrut +\mathstrut 84q^{40} \) \(\mathstrut -\mathstrut 20q^{41} \) \(\mathstrut +\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 48q^{44} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 368q^{49} \) \(\mathstrut +\mathstrut 34q^{50} \) \(\mathstrut +\mathstrut 20q^{52} \) \(\mathstrut -\mathstrut 4q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 8q^{56} \) \(\mathstrut +\mathstrut 4q^{58} \) \(\mathstrut -\mathstrut 44q^{59} \) \(\mathstrut -\mathstrut 16q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut +\mathstrut 234q^{64} \) \(\mathstrut -\mathstrut 64q^{65} \) \(\mathstrut +\mathstrut 16q^{67} \) \(\mathstrut +\mathstrut 46q^{68} \) \(\mathstrut -\mathstrut 20q^{70} \) \(\mathstrut -\mathstrut 64q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 40q^{74} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut +\mathstrut 12q^{79} \) \(\mathstrut -\mathstrut 44q^{80} \) \(\mathstrut +\mathstrut 100q^{83} \) \(\mathstrut -\mathstrut 48q^{85} \) \(\mathstrut -\mathstrut 8q^{86} \) \(\mathstrut -\mathstrut 72q^{88} \) \(\mathstrut -\mathstrut 4q^{89} \) \(\mathstrut -\mathstrut 12q^{91} \) \(\mathstrut -\mathstrut 16q^{92} \) \(\mathstrut +\mathstrut 16q^{95} \) \(\mathstrut -\mathstrut 78q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8037))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 19 47
8037.2.a.a \(1\) \(64.176\) \(\Q\) None \(-2\) \(0\) \(3\) \(1\) \(-\) \(-\) \(+\) \(q-2q^{2}+2q^{4}+3q^{5}+q^{7}-6q^{10}+\cdots\)
8037.2.a.b \(1\) \(64.176\) \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(+\) \(+\) \(q-2q^{4}-q^{5}-3q^{7}-3q^{11}-2q^{13}+\cdots\)
8037.2.a.c \(1\) \(64.176\) \(\Q\) None \(2\) \(0\) \(1\) \(1\) \(-\) \(+\) \(-\) \(q+2q^{2}+2q^{4}+q^{5}+q^{7}+2q^{10}+\cdots\)
8037.2.a.d \(1\) \(64.176\) \(\Q\) None \(2\) \(0\) \(3\) \(1\) \(-\) \(+\) \(+\) \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}+6q^{10}+\cdots\)
8037.2.a.e \(3\) \(64.176\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(-6\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{2})q^{5}+(-2+\cdots)q^{7}+\cdots\)
8037.2.a.f \(3\) \(64.176\) \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(3\) \(0\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1+\beta _{1}-\beta _{2})q^{5}+\cdots\)
8037.2.a.g \(4\) \(64.176\) 4.4.2777.1 None \(0\) \(0\) \(-2\) \(-5\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
8037.2.a.h \(4\) \(64.176\) 4.4.1957.1 None \(0\) \(0\) \(-5\) \(-5\) \(-\) \(+\) \(-\) \(q+(\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(1+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
8037.2.a.i \(6\) \(64.176\) 6.6.5476681.1 None \(-4\) \(0\) \(4\) \(2\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{4})q^{2}+(1+\beta _{2}+2\beta _{4})q^{4}+\cdots\)
8037.2.a.j \(7\) \(64.176\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(0\) \(-6\) \(-3\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{5})q^{5}+\cdots\)
8037.2.a.k \(7\) \(64.176\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(0\) \(6\) \(7\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
8037.2.a.l \(7\) \(64.176\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(0\) \(10\) \(3\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1})q^{2}+(1-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
8037.2.a.m \(12\) \(64.176\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(0\) \(7\) \(-13\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1+\beta _{6})q^{5}+\cdots\)
8037.2.a.n \(16\) \(64.176\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(4\) \(0\) \(1\) \(-9\) \(-\) \(+\) \(-\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+(-2+\cdots)q^{7}+\cdots\)
8037.2.a.o \(18\) \(64.176\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-1\) \(0\) \(-5\) \(3\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{10}q^{5}+(\beta _{14}+\cdots)q^{7}+\cdots\)
8037.2.a.p \(23\) \(64.176\) None \(-5\) \(0\) \(-12\) \(-2\) \(-\) \(-\) \(+\)
8037.2.a.q \(23\) \(64.176\) None \(-2\) \(0\) \(-9\) \(5\) \(-\) \(+\) \(+\)
8037.2.a.r \(23\) \(64.176\) None \(-1\) \(0\) \(-1\) \(15\) \(-\) \(-\) \(-\)
8037.2.a.s \(24\) \(64.176\) None \(-6\) \(0\) \(-10\) \(6\) \(-\) \(+\) \(-\)
8037.2.a.t \(24\) \(64.176\) None \(-2\) \(0\) \(2\) \(6\) \(-\) \(-\) \(-\)
8037.2.a.u \(34\) \(64.176\) None \(-5\) \(0\) \(-14\) \(0\) \(+\) \(-\) \(-\)
8037.2.a.v \(34\) \(64.176\) None \(-5\) \(0\) \(-6\) \(0\) \(+\) \(+\) \(+\)
8037.2.a.w \(34\) \(64.176\) None \(5\) \(0\) \(6\) \(0\) \(+\) \(+\) \(-\)
8037.2.a.x \(34\) \(64.176\) None \(5\) \(0\) \(14\) \(0\) \(+\) \(-\) \(+\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8037))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8037)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(423))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(893))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2679))\)\(^{\oplus 2}\)