Properties

Label 2432.2.a
Level $2432$
Weight $2$
Character orbit 2432.a
Rep. character $\chi_{2432}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $28$
Sturm bound $640$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2432 = 2^{7} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2432.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 28 \)
Sturm bound: \(640\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2432))\).

Total New Old
Modular forms 336 72 264
Cusp forms 305 72 233
Eisenstein series 31 0 31

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
\(+\)\(+\)$+$\(15\)
\(+\)\(-\)$-$\(21\)
\(-\)\(+\)$-$\(21\)
\(-\)\(-\)$+$\(15\)
Plus space\(+\)\(30\)
Minus space\(-\)\(42\)

Trace form

\( 72 q + 72 q^{9} + O(q^{10}) \) \( 72 q + 72 q^{9} + 16 q^{17} + 88 q^{25} + 16 q^{41} + 72 q^{49} - 32 q^{65} - 48 q^{73} + 136 q^{81} + 16 q^{89} + 80 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2432))\) 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 19
2432.2.a.a 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(-1\) \(-2\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-5q^{7}-2q^{9}-6q^{11}+\cdots\)
2432.2.a.b 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(-1\) \(-2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}-2q^{9}-2q^{11}+\cdots\)
2432.2.a.c 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}-2q^{9}-2q^{11}+\cdots\)
2432.2.a.d 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(-1\) \(2\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+5q^{7}-2q^{9}-6q^{11}+\cdots\)
2432.2.a.e 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(1\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}-2q^{9}+2q^{11}+\cdots\)
2432.2.a.f 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(1\) \(-2\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+5q^{7}-2q^{9}+6q^{11}+\cdots\)
2432.2.a.g 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(1\) \(2\) \(-5\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-5q^{7}-2q^{9}+6q^{11}+\cdots\)
2432.2.a.h 2432.a 1.a $1$ $19.420$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}-2q^{9}+2q^{11}+\cdots\)
2432.2.a.i 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(-1+2\beta )q^{7}+\cdots\)
2432.2.a.j 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(2\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(1-2\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
2432.2.a.k 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-4\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
2432.2.a.l 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(4\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
2432.2.a.m 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-4\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
2432.2.a.n 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(4\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+2q^{5}+(-2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
2432.2.a.o 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(1+2\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
2432.2.a.p 2432.a 1.a $2$ $19.420$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(-1-2\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
2432.2.a.q 2432.a 1.a $3$ $19.420$ 3.3.316.1 None \(0\) \(-1\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}-q^{7}+\beta _{2}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2432.2.a.r 2432.a 1.a $3$ $19.420$ 3.3.316.1 None \(0\) \(-1\) \(0\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-\beta _{2}q^{5}+q^{7}+\beta _{2}q^{9}+(-2+\cdots)q^{11}+\cdots\)
2432.2.a.s 2432.a 1.a $3$ $19.420$ 3.3.316.1 None \(0\) \(1\) \(0\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-q^{7}+\beta _{2}q^{9}+(2+\cdots)q^{11}+\cdots\)
2432.2.a.t 2432.a 1.a $3$ $19.420$ 3.3.316.1 None \(0\) \(1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+q^{7}+\beta _{2}q^{9}+(2+\cdots)q^{11}+\cdots\)
2432.2.a.u 2432.a 1.a $4$ $19.420$ 4.4.42848.1 None \(0\) \(0\) \(-2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
2432.2.a.v 2432.a 1.a $4$ $19.420$ 4.4.42848.1 None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
2432.2.a.w 2432.a 1.a $4$ $19.420$ 4.4.42848.1 None \(0\) \(0\) \(2\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
2432.2.a.x 2432.a 1.a $4$ $19.420$ 4.4.42848.1 None \(0\) \(0\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1+\beta _{2}+\beta _{3})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
2432.2.a.y 2432.a 1.a $5$ $19.420$ 5.5.7145312.1 None \(0\) \(-4\) \(-4\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)
2432.2.a.z 2432.a 1.a $5$ $19.420$ 5.5.7145312.1 None \(0\) \(-4\) \(4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{4})q^{5}+\beta _{2}q^{7}+\cdots\)
2432.2.a.ba 2432.a 1.a $5$ $19.420$ 5.5.7145312.1 None \(0\) \(4\) \(-4\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{4})q^{5}+\beta _{2}q^{7}+\cdots\)
2432.2.a.bb 2432.a 1.a $5$ $19.420$ 5.5.7145312.1 None \(0\) \(4\) \(4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(1-\beta _{4})q^{5}-\beta _{2}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2432))\) into lower level spaces

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