Properties

Label 4592.2.a
Level $4592$
Weight $2$
Character orbit 4592.a
Rep. character $\chi_{4592}(1,\cdot)$
Character field $\Q$
Dimension $120$
Newform subspaces $37$
Sturm bound $1344$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4592 = 2^{4} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4592.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1344\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4592))\).

Total New Old
Modular forms 684 120 564
Cusp forms 661 120 541
Eisenstein series 23 0 23

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

\(2\)\(7\)\(41\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(15\)
\(+\)\(+\)\(-\)\(-\)\(15\)
\(+\)\(-\)\(+\)\(-\)\(15\)
\(+\)\(-\)\(-\)\(+\)\(15\)
\(-\)\(+\)\(+\)\(-\)\(18\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(12\)
\(-\)\(-\)\(-\)\(-\)\(19\)
Plus space\(+\)\(53\)
Minus space\(-\)\(67\)

Trace form

\( 120q + 2q^{7} + 120q^{9} + O(q^{10}) \) \( 120q + 2q^{7} + 120q^{9} - 8q^{11} - 16q^{15} + 16q^{19} + 4q^{23} + 120q^{25} - 24q^{27} - 8q^{29} + 16q^{31} - 12q^{35} - 8q^{37} - 24q^{39} + 4q^{43} - 24q^{47} + 120q^{49} - 8q^{51} - 8q^{53} + 16q^{57} - 32q^{61} + 10q^{63} + 16q^{65} + 8q^{67} - 32q^{69} - 16q^{71} + 32q^{75} - 8q^{77} + 56q^{79} + 136q^{81} + 16q^{83} - 32q^{85} + 56q^{87} + 16q^{89} + 72q^{95} + 16q^{97} + 24q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4592))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7 41
4592.2.a.a \(1\) \(36.667\) \(\Q\) None \(0\) \(-3\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q-3q^{3}-q^{5}-q^{7}+6q^{9}-4q^{11}+\cdots\)
4592.2.a.b \(1\) \(36.667\) \(\Q\) None \(0\) \(-2\) \(-2\) \(1\) \(-\) \(-\) \(+\) \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+6q^{11}+\cdots\)
4592.2.a.c \(1\) \(36.667\) \(\Q\) None \(0\) \(-2\) \(2\) \(-1\) \(-\) \(+\) \(+\) \(q-2q^{3}+2q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
4592.2.a.d \(1\) \(36.667\) \(\Q\) None \(0\) \(-1\) \(-3\) \(-1\) \(-\) \(+\) \(-\) \(q-q^{3}-3q^{5}-q^{7}-2q^{9}+2q^{13}+\cdots\)
4592.2.a.e \(1\) \(36.667\) \(\Q\) None \(0\) \(-1\) \(-3\) \(1\) \(+\) \(-\) \(+\) \(q-q^{3}-3q^{5}+q^{7}-2q^{9}-6q^{11}+\cdots\)
4592.2.a.f \(1\) \(36.667\) \(\Q\) None \(0\) \(0\) \(-4\) \(-1\) \(-\) \(+\) \(+\) \(q-4q^{5}-q^{7}-3q^{9}+2q^{11}-6q^{13}+\cdots\)
4592.2.a.g \(1\) \(36.667\) \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) \(+\) \(+\) \(-\) \(q-2q^{5}-q^{7}-3q^{9}+2q^{13}+2q^{17}+\cdots\)
4592.2.a.h \(1\) \(36.667\) \(\Q\) None \(0\) \(1\) \(-1\) \(1\) \(-\) \(-\) \(-\) \(q+q^{3}-q^{5}+q^{7}-2q^{9}+6q^{11}-4q^{13}+\cdots\)
4592.2.a.i \(1\) \(36.667\) \(\Q\) None \(0\) \(1\) \(1\) \(-1\) \(-\) \(+\) \(-\) \(q+q^{3}+q^{5}-q^{7}-2q^{9}-2q^{11}+4q^{13}+\cdots\)
4592.2.a.j \(1\) \(36.667\) \(\Q\) None \(0\) \(1\) \(1\) \(1\) \(-\) \(-\) \(+\) \(q+q^{3}+q^{5}+q^{7}-2q^{9}+2q^{13}+q^{15}+\cdots\)
4592.2.a.k \(1\) \(36.667\) \(\Q\) None \(0\) \(2\) \(4\) \(-1\) \(-\) \(+\) \(+\) \(q+2q^{3}+4q^{5}-q^{7}+q^{9}-4q^{11}+\cdots\)
4592.2.a.l \(1\) \(36.667\) \(\Q\) None \(0\) \(3\) \(-1\) \(-1\) \(-\) \(+\) \(+\) \(q+3q^{3}-q^{5}-q^{7}+6q^{9}+2q^{11}+\cdots\)
4592.2.a.m \(2\) \(36.667\) \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(2\) \(-2\) \(-\) \(+\) \(-\) \(q-2q^{3}+(1+\beta )q^{5}-q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
4592.2.a.n \(2\) \(36.667\) \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(1\) \(2\) \(-\) \(-\) \(+\) \(q+\beta q^{3}+\beta q^{5}+q^{7}+(-2+\beta )q^{9}+\cdots\)
4592.2.a.o \(2\) \(36.667\) \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(-3\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+(1+\cdots)q^{9}+\cdots\)
4592.2.a.p \(2\) \(36.667\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-1\) \(-2\) \(-\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
4592.2.a.q \(2\) \(36.667\) \(\Q(\sqrt{5}) \) None \(0\) \(3\) \(-1\) \(-2\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+(-1+\cdots)q^{9}+\cdots\)
4592.2.a.r \(3\) \(36.667\) \(\Q(\zeta_{14})^+\) None \(0\) \(-5\) \(2\) \(3\) \(-\) \(-\) \(-\) \(q+(-2-\beta _{2})q^{3}+(2-2\beta _{1}+2\beta _{2})q^{5}+\cdots\)
4592.2.a.s \(3\) \(36.667\) 3.3.568.1 None \(0\) \(-1\) \(1\) \(3\) \(-\) \(-\) \(+\) \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(3-2\beta _{1}-\beta _{2})q^{9}+\cdots\)
4592.2.a.t \(3\) \(36.667\) 3.3.257.1 None \(0\) \(1\) \(6\) \(-3\) \(-\) \(+\) \(+\) \(q+(\beta _{1}-\beta _{2})q^{3}+2q^{5}-q^{7}+(3-\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.u \(3\) \(36.667\) 3.3.229.1 None \(0\) \(2\) \(-4\) \(-3\) \(+\) \(+\) \(+\) \(q+(1+\beta _{2})q^{3}+(-1-2\beta _{1}+\beta _{2})q^{5}+\cdots\)
4592.2.a.v \(3\) \(36.667\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q+(1-\beta _{1})q^{3}+(-2\beta _{1}+2\beta _{2})q^{5}-q^{7}+\cdots\)
4592.2.a.w \(3\) \(36.667\) \(\Q(\zeta_{18})^+\) None \(0\) \(3\) \(0\) \(3\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+2\beta _{2}q^{5}+q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.x \(4\) \(36.667\) 4.4.6809.1 None \(0\) \(0\) \(-3\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4592.2.a.y \(4\) \(36.667\) 4.4.107637.1 None \(0\) \(0\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4592.2.a.z \(4\) \(36.667\) 4.4.27329.1 None \(0\) \(1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{3}-q^{7}+(\beta _{1}+\beta _{2})q^{9}+(2-2\beta _{1}+\cdots)q^{11}+\cdots\)
4592.2.a.ba \(4\) \(36.667\) 4.4.11348.1 None \(0\) \(1\) \(3\) \(4\) \(-\) \(-\) \(-\) \(q+\beta _{2}q^{3}+(1-\beta _{2}+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bb \(5\) \(36.667\) 5.5.633117.1 None \(0\) \(-4\) \(-5\) \(-5\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{2}+\beta _{3})q^{5}+\cdots\)
4592.2.a.bc \(5\) \(36.667\) 5.5.287349.1 None \(0\) \(-2\) \(-3\) \(5\) \(-\) \(-\) \(+\) \(q-\beta _{2}q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+q^{7}+\cdots\)
4592.2.a.bd \(5\) \(36.667\) 5.5.1935333.1 None \(0\) \(-2\) \(3\) \(-5\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(1+\beta _{4})q^{5}-q^{7}+(1+\beta _{1}+\cdots)q^{9}+\cdots\)
4592.2.a.be \(5\) \(36.667\) 5.5.470117.1 None \(0\) \(2\) \(-1\) \(5\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+q^{7}+\cdots\)
4592.2.a.bf \(6\) \(36.667\) 6.6.23279501.1 None \(0\) \(-3\) \(-6\) \(6\) \(+\) \(-\) \(-\) \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{2})q^{5}+q^{7}+\cdots\)
4592.2.a.bg \(6\) \(36.667\) 6.6.185257757.1 None \(0\) \(4\) \(-1\) \(6\) \(-\) \(-\) \(-\) \(q+(1-\beta _{2})q^{3}+(\beta _{3}-\beta _{4})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bh \(7\) \(36.667\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(4\) \(5\) \(7\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(1+\beta _{3})q^{5}+q^{7}+(2+\cdots)q^{9}+\cdots\)
4592.2.a.bi \(8\) \(36.667\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(6\) \(-8\) \(+\) \(+\) \(+\) \(q+\beta _{3}q^{3}+(1+\beta _{6})q^{5}-q^{7}+(1-\beta _{3}+\cdots)q^{9}+\cdots\)
4592.2.a.bj \(8\) \(36.667\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(10\) \(-8\) \(+\) \(+\) \(-\) \(q-\beta _{5}q^{3}+(1+\beta _{1})q^{5}-q^{7}+(2+\beta _{7})q^{9}+\cdots\)
4592.2.a.bk \(9\) \(36.667\) \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-3\) \(-2\) \(9\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+q^{7}+(2+\beta _{2}-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(82))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2296))\)\(^{\oplus 2}\)