Properties

Label 4600.2.a
Level $4600$
Weight $2$
Character orbit 4600.a
Rep. character $\chi_{4600}(1,\cdot)$
Character field $\Q$
Dimension $104$
Newform subspaces $37$
Sturm bound $1440$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4600 = 2^{3} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4600.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 37 \)
Sturm bound: \(1440\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4600))\).

Total New Old
Modular forms 744 104 640
Cusp forms 697 104 593
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.

\(2\)\(5\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(13\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(14\)
\(+\)\(-\)\(-\)\(+\)\(12\)
\(-\)\(+\)\(+\)\(-\)\(12\)
\(-\)\(+\)\(-\)\(+\)\(11\)
\(-\)\(-\)\(+\)\(+\)\(13\)
\(-\)\(-\)\(-\)\(-\)\(15\)
Plus space\(+\)\(49\)
Minus space\(-\)\(55\)

Trace form

\( 104q - 8q^{7} + 96q^{9} + O(q^{10}) \) \( 104q - 8q^{7} + 96q^{9} + 2q^{11} - 4q^{13} + 2q^{19} - 4q^{21} - 12q^{27} + 16q^{29} - 20q^{31} - 12q^{33} + 10q^{37} + 20q^{39} + 4q^{41} - 10q^{43} - 4q^{47} + 112q^{49} + 40q^{51} - 18q^{53} - 32q^{57} + 48q^{59} + 14q^{61} + 20q^{63} + 6q^{67} - 4q^{69} + 28q^{71} - 16q^{73} - 8q^{77} - 68q^{79} + 88q^{81} + 14q^{83} + 20q^{87} + 12q^{89} - 60q^{91} + 4q^{93} - 16q^{97} + 74q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4600))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 5 23
4600.2.a.a \(1\) \(36.731\) \(\Q\) None \(0\) \(-3\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-3q^{3}+2q^{7}+6q^{9}+5q^{13}+6q^{17}+\cdots\)
4600.2.a.b \(1\) \(36.731\) \(\Q\) None \(0\) \(-2\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q-2q^{3}-3q^{7}+q^{9}-6q^{13}-7q^{17}+\cdots\)
4600.2.a.c \(1\) \(36.731\) \(\Q\) None \(0\) \(-2\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q-2q^{3}+q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
4600.2.a.d \(1\) \(36.731\) \(\Q\) None \(0\) \(-2\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q-2q^{3}+3q^{7}+q^{9}+5q^{11}+5q^{13}+\cdots\)
4600.2.a.e \(1\) \(36.731\) \(\Q\) None \(0\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-q^{3}-4q^{7}-2q^{9}+3q^{11}+2q^{13}+\cdots\)
4600.2.a.f \(1\) \(36.731\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}+2q^{7}-2q^{9}-q^{13}+4q^{17}+\cdots\)
4600.2.a.g \(1\) \(36.731\) \(\Q\) None \(0\) \(0\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-4q^{7}-3q^{9}+6q^{11}+2q^{13}-6q^{17}+\cdots\)
4600.2.a.h \(1\) \(36.731\) \(\Q\) None \(0\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q-q^{7}-3q^{9}-6q^{11}+2q^{13}+3q^{17}+\cdots\)
4600.2.a.i \(1\) \(36.731\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q+q^{3}-2q^{7}-2q^{9}-4q^{11}+5q^{13}+\cdots\)
4600.2.a.j \(1\) \(36.731\) \(\Q\) None \(0\) \(1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+q^{3}-2q^{9}+2q^{11}+5q^{13}+4q^{17}+\cdots\)
4600.2.a.k \(1\) \(36.731\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+q^{3}+4q^{7}-2q^{9}-2q^{11}-7q^{13}+\cdots\)
4600.2.a.l \(1\) \(36.731\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+4q^{7}-2q^{9}+3q^{11}-2q^{13}+\cdots\)
4600.2.a.m \(1\) \(36.731\) \(\Q\) None \(0\) \(2\) \(0\) \(-3\) \(-\) \(-\) \(+\) \(q+2q^{3}-3q^{7}+q^{9}+5q^{11}-5q^{13}+\cdots\)
4600.2.a.n \(1\) \(36.731\) \(\Q\) None \(0\) \(2\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q+2q^{3}-q^{7}+q^{9}-5q^{11}-q^{13}+\cdots\)
4600.2.a.o \(1\) \(36.731\) \(\Q\) None \(0\) \(2\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q+2q^{3}+3q^{7}+q^{9}+6q^{13}+7q^{17}+\cdots\)
4600.2.a.p \(1\) \(36.731\) \(\Q\) None \(0\) \(3\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+3q^{3}+2q^{7}+6q^{9}-q^{13}+6q^{21}+\cdots\)
4600.2.a.q \(2\) \(36.731\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+(-1-\beta )q^{3}+(2+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
4600.2.a.r \(2\) \(36.731\) \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{3}-2\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
4600.2.a.s \(2\) \(36.731\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta q^{3}+(1+\beta )q^{9}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
4600.2.a.t \(2\) \(36.731\) \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(0\) \(1\) \(-\) \(+\) \(-\) \(q+\beta q^{3}+(1-\beta )q^{7}+(1+\beta )q^{9}-2q^{11}+\cdots\)
4600.2.a.u \(2\) \(36.731\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(-2-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
4600.2.a.v \(3\) \(36.731\) 3.3.229.1 None \(0\) \(-2\) \(0\) \(-7\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{3}+(-2+\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
4600.2.a.w \(3\) \(36.731\) \(\Q(\zeta_{14})^+\) None \(0\) \(-2\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{2})q^{3}+(-2-2\beta _{2})q^{7}+(-1+\cdots)q^{9}+\cdots\)
4600.2.a.x \(3\) \(36.731\) 3.3.2597.1 None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-1+\beta _{1})q^{7}+(3+\beta _{2})q^{9}+\cdots\)
4600.2.a.y \(3\) \(36.731\) 3.3.621.1 None \(0\) \(0\) \(0\) \(-3\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{3}+(-1-\beta _{1})q^{7}+(1+\beta _{1}+\beta _{2})q^{9}+\cdots\)
4600.2.a.z \(3\) \(36.731\) \(\Q(\zeta_{14})^+\) None \(0\) \(2\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+(1-\beta _{1})q^{3}+(2-2\beta _{1})q^{7}+(-2\beta _{1}+\cdots)q^{9}+\cdots\)
4600.2.a.ba \(4\) \(36.731\) 4.4.15529.1 None \(0\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{7}+(2-2\beta _{1}+\cdots)q^{9}+\cdots\)
4600.2.a.bb \(4\) \(36.731\) 4.4.15529.1 None \(0\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(q-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{7}+(2-2\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4600.2.a.bc \(5\) \(36.731\) 5.5.791953.1 None \(0\) \(-3\) \(0\) \(1\) \(-\) \(-\) \(+\) \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2}+\beta _{4})q^{7}+\cdots\)
4600.2.a.bd \(5\) \(36.731\) 5.5.521397.1 None \(0\) \(0\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4600.2.a.be \(5\) \(36.731\) 5.5.13955077.1 None \(0\) \(0\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{3}+(\beta _{3}+\beta _{4})q^{7}+(2+\beta _{2}+\beta _{4})q^{9}+\cdots\)
4600.2.a.bf \(5\) \(36.731\) 5.5.521397.1 None \(0\) \(0\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(1+\beta _{2})q^{9}+\cdots\)
4600.2.a.bg \(5\) \(36.731\) 5.5.791953.1 None \(0\) \(3\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(q+(1-\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{4})q^{7}+\cdots\)
4600.2.a.bh \(7\) \(36.731\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(0\) \(-4\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\cdots)q^{9}+\cdots\)
4600.2.a.bi \(7\) \(36.731\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(0\) \(4\) \(-\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{3})q^{7}+(\beta _{2}+\beta _{5}+\beta _{6})q^{9}+\cdots\)
4600.2.a.bj \(8\) \(36.731\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-3\) \(0\) \(-7\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-1-\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)
4600.2.a.bk \(8\) \(36.731\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(3\) \(0\) \(7\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(1+\beta _{7})q^{7}+(2+\beta _{3}+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4600))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4600)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(230))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(920))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2300))\)\(^{\oplus 2}\)