Properties

Label 4508.2.a
Level $4508$
Weight $2$
Character orbit 4508.a
Rep. character $\chi_{4508}(1,\cdot)$
Character field $\Q$
Dimension $74$
Newform subspaces $15$
Sturm bound $1344$
Trace bound $15$

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Defining parameters

Level: \( N \) \(=\) \( 4508 = 2^{2} \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4508.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(1344\)
Trace bound: \(15\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4508))\).

Total New Old
Modular forms 696 74 622
Cusp forms 649 74 575
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.

\(2\)\(7\)\(23\)FrickeDim.
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(17\)
\(-\)\(-\)\(+\)\(+\)\(20\)
\(-\)\(-\)\(-\)\(-\)\(20\)
Plus space\(+\)\(37\)
Minus space\(-\)\(37\)

Trace form

\( 74 q - 2 q^{3} - 2 q^{5} + 64 q^{9} + O(q^{10}) \) \( 74 q - 2 q^{3} - 2 q^{5} + 64 q^{9} - 6 q^{11} - 6 q^{13} - 6 q^{15} - 6 q^{17} - 12 q^{19} + 66 q^{25} - 2 q^{27} - 14 q^{29} + 6 q^{31} - 18 q^{33} + 14 q^{37} + 14 q^{39} - 6 q^{41} + 28 q^{43} - 12 q^{45} - 2 q^{47} + 14 q^{51} - 36 q^{53} + 24 q^{55} + 48 q^{57} - 12 q^{59} - 4 q^{61} - 50 q^{65} + 2 q^{67} + 4 q^{69} + 14 q^{71} + 6 q^{73} + 10 q^{75} + 28 q^{79} + 50 q^{81} + 18 q^{83} - 60 q^{85} + 30 q^{87} - 12 q^{89} + 18 q^{93} + 12 q^{95} - 34 q^{97} - 116 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4508))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7 23
4508.2.a.a 4508.a 1.a $1$ $35.997$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+q^{13}+6q^{17}-2q^{19}+\cdots\)
4508.2.a.b 4508.a 1.a $1$ $35.997$ \(\Q\) None \(0\) \(-1\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-2q^{9}-2q^{11}+q^{13}+\cdots\)
4508.2.a.c 4508.a 1.a $1$ $35.997$ \(\Q\) None \(0\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}-2q^{11}+3q^{13}-q^{23}+\cdots\)
4508.2.a.d 4508.a 1.a $1$ $35.997$ \(\Q\) None \(0\) \(3\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}+6q^{9}+2q^{11}+5q^{13}+\cdots\)
4508.2.a.e 4508.a 1.a $4$ $35.997$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{9}-2\beta _{2}q^{11}+\cdots\)
4508.2.a.f 4508.a 1.a $5$ $35.997$ 5.5.6963152.1 None \(0\) \(-3\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{2}-\beta _{3})q^{5}+\cdots\)
4508.2.a.g 4508.a 1.a $5$ $35.997$ 5.5.8580816.1 None \(0\) \(-1\) \(-4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{4})q^{5}+(2+\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
4508.2.a.h 4508.a 1.a $6$ $35.997$ 6.6.217653248.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{5})q^{5}+(1+\beta _{2}+\cdots)q^{9}+\cdots\)
4508.2.a.i 4508.a 1.a $6$ $35.997$ 6.6.524361728.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+(1+\beta _{2})q^{9}+\cdots\)
4508.2.a.j 4508.a 1.a $6$ $35.997$ 6.6.73156608.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{5})q^{5}+(1+\beta _{3}+\cdots)q^{9}+\cdots\)
4508.2.a.k 4508.a 1.a $7$ $35.997$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-5\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4508.2.a.l 4508.a 1.a $7$ $35.997$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-3\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{3}-\beta _{5}q^{5}+(1+\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{9}+\cdots\)
4508.2.a.m 4508.a 1.a $7$ $35.997$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(3\) \(2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{3}+\beta _{5}q^{5}+(1+\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{9}+\cdots\)
4508.2.a.n 4508.a 1.a $7$ $35.997$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(5\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-\beta _{5}q^{5}+(1-\beta _{1}+\beta _{2}+\cdots)q^{9}+\cdots\)
4508.2.a.o 4508.a 1.a $10$ $35.997$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{2}q^{9}+(\beta _{5}+\beta _{6}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4508))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4508)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(322))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(644))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1127))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2254))\)\(^{\oplus 2}\)