Properties

Label 8048.2.a
Level 8048
Weight 2
Character orbit a
Rep. character \(\chi_{8048}(1,\cdot)\)
Character field \(\Q\)
Dimension 251
Newforms 25
Sturm bound 2016
Trace bound 13

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Defining parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)
Character field: \(\Q\)
Newforms: \( 25 \)
Sturm bound: \(2016\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8048))\).

Total New Old
Modular forms 1014 251 763
Cusp forms 1003 251 752
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.

\(2\)\(503\)FrickeDim.
\(+\)\(+\)\(+\)\(63\)
\(+\)\(-\)\(-\)\(63\)
\(-\)\(+\)\(-\)\(73\)
\(-\)\(-\)\(+\)\(52\)
Plus space\(+\)\(115\)
Minus space\(-\)\(136\)

Trace form

\(251q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 247q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(251q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 247q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 12q^{15} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 10q^{23} \) \(\mathstrut +\mathstrut 245q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 16q^{39} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 10q^{45} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 251q^{49} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 16q^{55} \) \(\mathstrut -\mathstrut 8q^{57} \) \(\mathstrut +\mathstrut 18q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 22q^{63} \) \(\mathstrut -\mathstrut 4q^{65} \) \(\mathstrut -\mathstrut 10q^{67} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut -\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 46q^{75} \) \(\mathstrut +\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 227q^{81} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 28q^{85} \) \(\mathstrut +\mathstrut 24q^{87} \) \(\mathstrut -\mathstrut 2q^{89} \) \(\mathstrut +\mathstrut 56q^{91} \) \(\mathstrut +\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 2q^{97} \) \(\mathstrut +\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8048))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 503
8048.2.a.a \(1\) \(64.264\) \(\Q\) None \(0\) \(-3\) \(-2\) \(-3\) \(-\) \(+\) \(q-3q^{3}-2q^{5}-3q^{7}+6q^{9}-3q^{11}+\cdots\)
8048.2.a.b \(1\) \(64.264\) \(\Q\) None \(0\) \(-1\) \(-4\) \(-1\) \(-\) \(+\) \(q-q^{3}-4q^{5}-q^{7}-2q^{9}+3q^{11}+\cdots\)
8048.2.a.c \(1\) \(64.264\) \(\Q\) None \(0\) \(-1\) \(-4\) \(3\) \(-\) \(+\) \(q-q^{3}-4q^{5}+3q^{7}-2q^{9}-5q^{11}+\cdots\)
8048.2.a.d \(1\) \(64.264\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(-\) \(-\) \(q-q^{3}-2q^{5}-q^{7}-2q^{9}-q^{11}-3q^{13}+\cdots\)
8048.2.a.e \(1\) \(64.264\) \(\Q\) None \(0\) \(-1\) \(-2\) \(3\) \(-\) \(-\) \(q-q^{3}-2q^{5}+3q^{7}-2q^{9}-q^{11}+\cdots\)
8048.2.a.f \(1\) \(64.264\) \(\Q\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q-3q^{9}-4q^{11}+2q^{13}-2q^{17}+2q^{19}+\cdots\)
8048.2.a.g \(1\) \(64.264\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+5q^{11}-5q^{13}+\cdots\)
8048.2.a.h \(1\) \(64.264\) \(\Q\) None \(0\) \(1\) \(0\) \(-1\) \(+\) \(+\) \(q+q^{3}-q^{7}-2q^{9}+5q^{11}+3q^{13}+\cdots\)
8048.2.a.i \(1\) \(64.264\) \(\Q\) None \(0\) \(1\) \(0\) \(5\) \(+\) \(-\) \(q+q^{3}+5q^{7}-2q^{9}+5q^{11}+q^{13}+\cdots\)
8048.2.a.j \(1\) \(64.264\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(+\) \(+\) \(q+q^{3}+2q^{5}-q^{7}-2q^{9}-3q^{11}+\cdots\)
8048.2.a.k \(1\) \(64.264\) \(\Q\) None \(0\) \(3\) \(0\) \(3\) \(-\) \(+\) \(q+3q^{3}+3q^{7}+6q^{9}-q^{11}+5q^{13}+\cdots\)
8048.2.a.l \(2\) \(64.264\) \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(4\) \(-\) \(-\) \(q-\beta q^{3}+(-1+\beta )q^{5}+(2+\beta )q^{7}+2q^{9}+\cdots\)
8048.2.a.m \(3\) \(64.264\) 3.3.257.1 None \(0\) \(-1\) \(0\) \(-1\) \(-\) \(+\) \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+\beta _{2}q^{9}+\cdots\)
8048.2.a.n \(5\) \(64.264\) 5.5.36497.1 None \(0\) \(0\) \(-1\) \(-3\) \(-\) \(-\) \(q+(-\beta _{1}+\beta _{3}-\beta _{4})q^{3}+(\beta _{2}+\beta _{3})q^{5}+\cdots\)
8048.2.a.o \(5\) \(64.264\) 5.5.205225.1 None \(0\) \(4\) \(-3\) \(9\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(-1-\beta _{1}-\beta _{3}-\beta _{4})q^{5}+\cdots\)
8048.2.a.p \(10\) \(64.264\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(8\) \(-1\) \(5\) \(-\) \(-\) \(q+(1-\beta _{1})q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
8048.2.a.q \(12\) \(64.264\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-5\) \(5\) \(-8\) \(-\) \(-\) \(q-\beta _{1}q^{3}-\beta _{9}q^{5}+(-1-\beta _{10})q^{7}+\cdots\)
8048.2.a.r \(12\) \(64.264\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(3\) \(7\) \(2\) \(-\) \(+\) \(q+\beta _{4}q^{3}+(\beta _{7}-\beta _{10})q^{5}+(-\beta _{2}+\beta _{6}+\cdots)q^{7}+\cdots\)
8048.2.a.s \(21\) \(64.264\) None \(0\) \(-10\) \(3\) \(-13\) \(-\) \(-\)
8048.2.a.t \(21\) \(64.264\) None \(0\) \(10\) \(-3\) \(15\) \(-\) \(+\)
8048.2.a.u \(26\) \(64.264\) None \(0\) \(-4\) \(9\) \(-11\) \(-\) \(+\)
8048.2.a.v \(28\) \(64.264\) None \(0\) \(-2\) \(-12\) \(0\) \(+\) \(+\)
8048.2.a.w \(29\) \(64.264\) None \(0\) \(7\) \(-4\) \(13\) \(+\) \(-\)
8048.2.a.x \(33\) \(64.264\) None \(0\) \(-10\) \(0\) \(-12\) \(+\) \(+\)
8048.2.a.y \(33\) \(64.264\) None \(0\) \(2\) \(12\) \(-4\) \(+\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8048))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8048)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(503))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1006))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2012))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\)\(^{\oplus 2}\)