Properties

Label 2368.2.a
Level $2368$
Weight $2$
Character orbit 2368.a
Rep. character $\chi_{2368}(1,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $36$
Sturm bound $608$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2368 = 2^{6} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2368.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 36 \)
Sturm bound: \(608\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2368))\).

Total New Old
Modular forms 316 72 244
Cusp forms 293 72 221
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.

\(2\)\(37\)FrickeDim.
\(+\)\(+\)\(+\)\(17\)
\(+\)\(-\)\(-\)\(19\)
\(-\)\(+\)\(-\)\(19\)
\(-\)\(-\)\(+\)\(17\)
Plus space\(+\)\(34\)
Minus space\(-\)\(38\)

Trace form

\( 72 q + 72 q^{9} + O(q^{10}) \) \( 72 q + 72 q^{9} + 72 q^{25} - 16 q^{33} - 16 q^{41} + 72 q^{49} - 16 q^{57} - 32 q^{61} - 32 q^{69} + 48 q^{77} + 24 q^{81} + 16 q^{85} - 32 q^{89} - 48 q^{93} - 32 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2368))\) 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 37
2368.2.a.a 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-3\) \(-4\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{5}-3q^{7}+6q^{9}+3q^{11}+\cdots\)
2368.2.a.b 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-3\) \(2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{5}+q^{7}+6q^{9}-5q^{11}+\cdots\)
2368.2.a.c 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-3\) \(4\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{5}+q^{7}+6q^{9}+3q^{11}+\cdots\)
2368.2.a.d 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}-3q^{11}+4q^{13}+\cdots\)
2368.2.a.e 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{7}-2q^{9}+q^{11}+2q^{13}+\cdots\)
2368.2.a.f 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{7}-2q^{9}-3q^{11}+2q^{17}+\cdots\)
2368.2.a.g 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-1\) \(2\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}-2q^{9}+q^{11}+6q^{13}+\cdots\)
2368.2.a.h 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(-1\) \(4\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+3q^{7}-2q^{9}+5q^{11}+\cdots\)
2368.2.a.i 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(0\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}-3q^{9}-2q^{13}+2q^{17}+\cdots\)
2368.2.a.j 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(0\) \(-2\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-3q^{9}-2q^{13}+2q^{17}+\cdots\)
2368.2.a.k 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(1\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{7}-2q^{9}+3q^{11}+2q^{17}+\cdots\)
2368.2.a.l 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}-2q^{9}-q^{11}+2q^{13}+\cdots\)
2368.2.a.m 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(1\) \(0\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots\)
2368.2.a.n 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(1\) \(2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
2368.2.a.o 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(1\) \(4\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-3q^{7}-2q^{9}-5q^{11}+\cdots\)
2368.2.a.p 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(3\) \(-4\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{5}+3q^{7}+6q^{9}-3q^{11}+\cdots\)
2368.2.a.q 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(3\) \(2\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{5}-q^{7}+6q^{9}+5q^{11}+\cdots\)
2368.2.a.r 2368.a 1.a $1$ $18.909$ \(\Q\) None \(0\) \(3\) \(4\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{5}-q^{7}+6q^{9}-3q^{11}+\cdots\)
2368.2.a.s 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{13}) \) None \(0\) \(-3\) \(1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+(2-2\beta )q^{7}+\cdots\)
2368.2.a.t 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{17}) \) None \(0\) \(-1\) \(-4\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2q^{5}-\beta q^{7}+(1+\beta )q^{9}+\beta q^{11}+\cdots\)
2368.2.a.u 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{5}) \) None \(0\) \(-1\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(1-3\beta )q^{5}+2\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
2368.2.a.v 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{13}) \) None \(0\) \(-1\) \(-1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+2\beta q^{7}+\beta q^{9}+\cdots\)
2368.2.a.w 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2q^{5}-\beta q^{7}+2q^{9}+\beta q^{11}+\cdots\)
2368.2.a.x 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(-4\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-2q^{5}+\beta q^{7}+(1+\beta )q^{9}-\beta q^{11}+\cdots\)
2368.2.a.y 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{5}) \) None \(0\) \(1\) \(-1\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(1-3\beta )q^{5}-2\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
2368.2.a.z 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{13}) \) None \(0\) \(1\) \(-1\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-1+\beta )q^{5}-2\beta q^{7}+\beta q^{9}+\cdots\)
2368.2.a.ba 2368.a 1.a $2$ $18.909$ \(\Q(\sqrt{13}) \) None \(0\) \(3\) \(1\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+\beta q^{5}+(-2+2\beta )q^{7}+\cdots\)
2368.2.a.bb 2368.a 1.a $3$ $18.909$ 3.3.229.1 None \(0\) \(-2\) \(1\) \(7\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{3}-\beta _{2}q^{5}+(2+\beta _{1}-\beta _{2})q^{7}+\cdots\)
2368.2.a.bc 2368.a 1.a $3$ $18.909$ 3.3.621.1 None \(0\) \(0\) \(3\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
2368.2.a.bd 2368.a 1.a $3$ $18.909$ 3.3.621.1 None \(0\) \(0\) \(3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(1-\beta _{1})q^{5}+(1-\beta _{2})q^{7}+\cdots\)
2368.2.a.be 2368.a 1.a $3$ $18.909$ 3.3.229.1 None \(0\) \(2\) \(1\) \(-7\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-\beta _{2}q^{5}+(-2-\beta _{1}+\beta _{2})q^{7}+\cdots\)
2368.2.a.bf 2368.a 1.a $4$ $18.909$ 4.4.2225.1 None \(0\) \(-3\) \(-3\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
2368.2.a.bg 2368.a 1.a $4$ $18.909$ 4.4.48389.1 None \(0\) \(-2\) \(-5\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1+\beta _{3})q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
2368.2.a.bh 2368.a 1.a $4$ $18.909$ 4.4.48389.1 None \(0\) \(2\) \(-5\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{3})q^{5}+(\beta _{2}-\beta _{3})q^{7}+\cdots\)
2368.2.a.bi 2368.a 1.a $4$ $18.909$ 4.4.2225.1 None \(0\) \(3\) \(-3\) \(-6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+(-1+\beta _{1}-\beta _{3})q^{5}+\cdots\)
2368.2.a.bj 2368.a 1.a $8$ $18.909$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{6}q^{5}-\beta _{4}q^{7}+(2+\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(148))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(592))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1184))\)\(^{\oplus 2}\)