Properties

Label 4864.2.a
Level $4864$
Weight $2$
Character orbit 4864.a
Rep. character $\chi_{4864}(1,\cdot)$
Character field $\Q$
Dimension $144$
Newform subspaces $46$
Sturm bound $1280$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4864 = 2^{8} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4864.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1280\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4864))\).

Total New Old
Modular forms 664 144 520
Cusp forms 617 144 473
Eisenstein series 47 0 47

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

\(2\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(34\)
\(+\)\(-\)\(-\)\(40\)
\(-\)\(+\)\(-\)\(38\)
\(-\)\(-\)\(+\)\(32\)
Plus space\(+\)\(66\)
Minus space\(-\)\(78\)

Trace form

\( 144q + 144q^{9} + O(q^{10}) \) \( 144q + 144q^{9} + 144q^{25} + 144q^{49} - 32q^{65} - 32q^{73} + 144q^{81} - 32q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4864))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
4864.2.a.a \(1\) \(38.839\) \(\Q\) None \(0\) \(-3\) \(-4\) \(1\) \(-\) \(+\) \(q-3q^{3}-4q^{5}+q^{7}+6q^{9}-5q^{13}+\cdots\)
4864.2.a.b \(1\) \(38.839\) \(\Q\) None \(0\) \(-3\) \(4\) \(-1\) \(-\) \(+\) \(q-3q^{3}+4q^{5}-q^{7}+6q^{9}+5q^{13}+\cdots\)
4864.2.a.c \(1\) \(38.839\) \(\Q\) None \(0\) \(-1\) \(-2\) \(-1\) \(-\) \(+\) \(q-q^{3}-2q^{5}-q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.d \(1\) \(38.839\) \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) \(-\) \(-\) \(q-q^{3}-3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots\)
4864.2.a.e \(1\) \(38.839\) \(\Q\) None \(0\) \(-1\) \(0\) \(3\) \(-\) \(-\) \(q-q^{3}+3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots\)
4864.2.a.f \(1\) \(38.839\) \(\Q\) None \(0\) \(-1\) \(2\) \(1\) \(+\) \(+\) \(q-q^{3}+2q^{5}+q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.g \(1\) \(38.839\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(-\) \(q-2q^{7}-3q^{9}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
4864.2.a.h \(1\) \(38.839\) \(\Q\) None \(0\) \(0\) \(0\) \(-2\) \(+\) \(+\) \(q-2q^{7}-3q^{9}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
4864.2.a.i \(1\) \(38.839\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(-\) \(q+2q^{7}-3q^{9}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
4864.2.a.j \(1\) \(38.839\) \(\Q\) None \(0\) \(0\) \(0\) \(2\) \(-\) \(+\) \(q+2q^{7}-3q^{9}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
4864.2.a.k \(1\) \(38.839\) \(\Q\) None \(0\) \(1\) \(-2\) \(1\) \(-\) \(-\) \(q+q^{3}-2q^{5}+q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.l \(1\) \(38.839\) \(\Q\) None \(0\) \(1\) \(0\) \(-3\) \(+\) \(+\) \(q+q^{3}-3q^{7}-2q^{9}+3q^{13}+3q^{17}+\cdots\)
4864.2.a.m \(1\) \(38.839\) \(\Q\) None \(0\) \(1\) \(0\) \(3\) \(+\) \(+\) \(q+q^{3}+3q^{7}-2q^{9}-3q^{13}+3q^{17}+\cdots\)
4864.2.a.n \(1\) \(38.839\) \(\Q\) None \(0\) \(1\) \(2\) \(-1\) \(+\) \(-\) \(q+q^{3}+2q^{5}-q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.o \(1\) \(38.839\) \(\Q\) None \(0\) \(3\) \(-4\) \(-1\) \(+\) \(-\) \(q+3q^{3}-4q^{5}-q^{7}+6q^{9}-5q^{13}+\cdots\)
4864.2.a.p \(1\) \(38.839\) \(\Q\) None \(0\) \(3\) \(4\) \(1\) \(+\) \(-\) \(q+3q^{3}+4q^{5}+q^{7}+6q^{9}+5q^{13}+\cdots\)
4864.2.a.q \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) \(+\) \(+\) \(q-2q^{3}-\beta q^{5}-\beta q^{7}+q^{9}+3q^{11}+\cdots\)
4864.2.a.r \(2\) \(38.839\) \(\Q(\sqrt{11}) \) None \(0\) \(-4\) \(0\) \(0\) \(+\) \(-\) \(q-2q^{3}+\beta q^{5}-\beta q^{7}+q^{9}+5q^{11}+\cdots\)
4864.2.a.s \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-4\) \(2\) \(+\) \(+\) \(q-q^{3}-2q^{5}+(1+\beta )q^{7}-2q^{9}+4q^{11}+\cdots\)
4864.2.a.t \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(-\) \(q-q^{3}-2\beta q^{5}-\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots\)
4864.2.a.u \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(4\) \(-2\) \(-\) \(+\) \(q-q^{3}+2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots\)
4864.2.a.v \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-4\) \(-2\) \(+\) \(-\) \(q+q^{3}-2q^{5}+(-1+\beta )q^{7}-2q^{9}+\cdots\)
4864.2.a.w \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) \(+\) \(+\) \(q+q^{3}-2\beta q^{5}+\beta q^{7}-2q^{9}+3\beta q^{13}+\cdots\)
4864.2.a.x \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(4\) \(2\) \(-\) \(-\) \(q+q^{3}+2q^{5}+(1-\beta )q^{7}-2q^{9}-4q^{11}+\cdots\)
4864.2.a.y \(2\) \(38.839\) \(\Q(\sqrt{11}) \) None \(0\) \(4\) \(0\) \(0\) \(-\) \(+\) \(q+2q^{3}+\beta q^{5}+\beta q^{7}+q^{9}-5q^{11}+\cdots\)
4864.2.a.z \(2\) \(38.839\) \(\Q(\sqrt{3}) \) None \(0\) \(4\) \(0\) \(0\) \(-\) \(-\) \(q+2q^{3}-\beta q^{5}+\beta q^{7}+q^{9}-3q^{11}+\cdots\)
4864.2.a.ba \(3\) \(38.839\) 3.3.316.1 None \(0\) \(-2\) \(-4\) \(-4\) \(-\) \(-\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots\)
4864.2.a.bb \(3\) \(38.839\) 3.3.316.1 None \(0\) \(-2\) \(4\) \(4\) \(+\) \(-\) \(q+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{1})q^{5}+\cdots\)
4864.2.a.bc \(3\) \(38.839\) 3.3.892.1 None \(0\) \(-1\) \(-2\) \(-3\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
4864.2.a.bd \(3\) \(38.839\) 3.3.892.1 None \(0\) \(-1\) \(2\) \(3\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4864.2.a.be \(3\) \(38.839\) 3.3.892.1 None \(0\) \(1\) \(-2\) \(3\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-1+\beta _{1})q^{5}+(1+\beta _{2})q^{7}+\cdots\)
4864.2.a.bf \(3\) \(38.839\) 3.3.892.1 None \(0\) \(1\) \(2\) \(-3\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(-1-\beta _{2})q^{7}+\cdots\)
4864.2.a.bg \(3\) \(38.839\) 3.3.316.1 None \(0\) \(2\) \(-4\) \(4\) \(-\) \(+\) \(q+(1-\beta _{1}+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+\cdots\)
4864.2.a.bh \(3\) \(38.839\) 3.3.316.1 None \(0\) \(2\) \(4\) \(-4\) \(+\) \(+\) \(q+(1-\beta _{1}+\beta _{2})q^{3}+(1+\beta _{1})q^{5}+(-1+\cdots)q^{7}+\cdots\)
4864.2.a.bi \(4\) \(38.839\) \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(-2\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
4864.2.a.bj \(4\) \(38.839\) \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{5}-\beta _{2}q^{7}-3q^{9}+(-2-\beta _{3})q^{11}+\cdots\)
4864.2.a.bk \(4\) \(38.839\) \(\Q(\sqrt{3}, \sqrt{19})\) None \(0\) \(0\) \(0\) \(0\) \(-\) \(+\) \(q+\beta _{1}q^{5}+\beta _{2}q^{7}-3q^{9}+(2+\beta _{3})q^{11}+\cdots\)
4864.2.a.bl \(4\) \(38.839\) \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(2\) \(0\) \(0\) \(-\) \(+\) \(q+(1+\beta _{3})q^{3}-\beta _{1}q^{5}+(2\beta _{1}-\beta _{2})q^{7}+\cdots\)
4864.2.a.bm \(8\) \(38.839\) 8.8.\(\cdots\).1 None \(0\) \(-4\) \(0\) \(0\) \(-\) \(-\) \(q+\beta _{1}q^{3}+\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots\)
4864.2.a.bn \(8\) \(38.839\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-8\) \(-4\) \(-\) \(-\) \(q-\beta _{5}q^{3}+(-1+\beta _{2})q^{5}-\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bo \(8\) \(38.839\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-8\) \(4\) \(+\) \(+\) \(q+\beta _{5}q^{3}+(-1+\beta _{2})q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bp \(8\) \(38.839\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(8\) \(-4\) \(-\) \(+\) \(q+\beta _{5}q^{3}+(1-\beta _{2})q^{5}-\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots\)
4864.2.a.bq \(8\) \(38.839\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(8\) \(4\) \(+\) \(-\) \(q-\beta _{5}q^{3}+(1-\beta _{2})q^{5}+\beta _{4}q^{7}+(1-\beta _{7})q^{9}+\cdots\)
4864.2.a.br \(8\) \(38.839\) 8.8.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) \(-\) \(+\) \(q-\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+(-\beta _{1}+\beta _{7})q^{9}+\cdots\)
4864.2.a.bs \(10\) \(38.839\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) \(+\) \(+\) \(q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{6})q^{7}+(1+\cdots)q^{9}+\cdots\)
4864.2.a.bt \(10\) \(38.839\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(4\) \(0\) \(0\) \(+\) \(-\) \(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(76))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(304))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2432))\)\(^{\oplus 2}\)