Properties

Label 3744.2.a
Level $3744$
Weight $2$
Character orbit 3744.a
Rep. character $\chi_{3744}(1,\cdot)$
Character field $\Q$
Dimension $60$
Newform subspaces $32$
Sturm bound $1344$
Trace bound $29$

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Defining parameters

Level: \( N \) \(=\) \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3744.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 32 \)
Sturm bound: \(1344\)
Trace bound: \(29\)
Distinguishing \(T_p\): \(5\), \(7\), \(11\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3744))\).

Total New Old
Modular forms 704 60 644
Cusp forms 641 60 581
Eisenstein series 63 0 63

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

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(6\)
\(+\)\(-\)\(+\)\(-\)\(10\)
\(+\)\(-\)\(-\)\(+\)\(7\)
\(-\)\(+\)\(+\)\(-\)\(6\)
\(-\)\(+\)\(-\)\(+\)\(6\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(27\)
Minus space\(-\)\(33\)

Trace form

\( 60 q + O(q^{10}) \) \( 60 q - 8 q^{17} + 44 q^{25} - 16 q^{29} + 24 q^{41} + 44 q^{49} + 56 q^{53} + 8 q^{61} + 8 q^{73} - 40 q^{77} - 80 q^{85} + 40 q^{89} + 72 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3744))\) 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 3 13
3744.2.a.a 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-2q^{11}-q^{13}-6q^{17}+\cdots\)
3744.2.a.b 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{11}+q^{13}+4q^{19}-4q^{23}+\cdots\)
3744.2.a.c 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{11}+q^{13}-4q^{19}+4q^{23}+\cdots\)
3744.2.a.d 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}+2q^{11}-q^{13}-6q^{17}+\cdots\)
3744.2.a.e 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{7}+2q^{11}+q^{13}+3q^{17}+\cdots\)
3744.2.a.f 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(-1\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{5}+3q^{7}-2q^{11}+q^{13}+3q^{17}+\cdots\)
3744.2.a.g 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+q^{13}-2q^{17}+2q^{19}+8q^{23}+\cdots\)
3744.2.a.h 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}+q^{13}+6q^{17}-6q^{19}+\cdots\)
3744.2.a.i 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-4q^{11}+q^{13}+6q^{17}+6q^{19}+\cdots\)
3744.2.a.j 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+q^{13}-2q^{17}-2q^{19}-8q^{23}+\cdots\)
3744.2.a.k 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-6q^{11}-q^{13}+2q^{17}+\cdots\)
3744.2.a.l 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{11}+q^{13}+6q^{17}-8q^{19}+\cdots\)
3744.2.a.m 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{11}+q^{13}-4q^{19}-4q^{23}+\cdots\)
3744.2.a.n 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{11}+q^{13}+4q^{19}+4q^{23}+\cdots\)
3744.2.a.o 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{11}+q^{13}+6q^{17}+8q^{19}+\cdots\)
3744.2.a.p 3744.a 1.a $1$ $29.896$ \(\Q\) None \(0\) \(0\) \(2\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+6q^{11}-q^{13}+2q^{17}+\cdots\)
3744.2.a.q 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-6\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-3q^{5}-\beta q^{7}-2\beta q^{11}-q^{13}+3q^{17}+\cdots\)
3744.2.a.r 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(-1-\beta )q^{7}+2q^{11}+\cdots\)
3744.2.a.s 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{5}+(1+\beta )q^{7}-2q^{11}+\cdots\)
3744.2.a.t 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{7}-\beta q^{11}-q^{13}+\beta q^{19}-2\beta q^{23}+\cdots\)
3744.2.a.u 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{7}+\beta q^{11}-q^{13}+\beta q^{19}+2\beta q^{23}+\cdots\)
3744.2.a.v 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-3+\beta )q^{7}-2\beta q^{11}+\cdots\)
3744.2.a.w 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(2\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(3-\beta )q^{7}+2\beta q^{11}-q^{13}+\cdots\)
3744.2.a.x 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(-1-\beta )q^{7}+2q^{11}+\cdots\)
3744.2.a.y 3744.a 1.a $2$ $29.896$ \(\Q(\sqrt{17}) \) None \(0\) \(0\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{5}+(1+\beta )q^{7}-2q^{11}-q^{13}+\cdots\)
3744.2.a.z 3744.a 1.a $3$ $29.896$ 3.3.148.1 None \(0\) \(0\) \(-2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}-\beta _{2}q^{7}+(-1+\beta _{1}+\cdots)q^{11}+\cdots\)
3744.2.a.ba 3744.a 1.a $3$ $29.896$ 3.3.148.1 None \(0\) \(0\) \(-2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}+(1-\beta _{1}-\beta _{2})q^{11}+\cdots\)
3744.2.a.bb 3744.a 1.a $4$ $29.896$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(-4\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{3})q^{5}-\beta _{2}q^{7}+(\beta _{1}+\beta _{2}+\cdots)q^{11}+\cdots\)
3744.2.a.bc 3744.a 1.a $4$ $29.896$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}+\beta _{3}q^{7}+(-2-\beta _{2})q^{11}+\cdots\)
3744.2.a.bd 3744.a 1.a $4$ $29.896$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(2+\beta _{2})q^{11}-q^{13}+\cdots\)
3744.2.a.be 3744.a 1.a $4$ $29.896$ 4.4.13448.1 None \(0\) \(0\) \(2\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\beta _{1}q^{11}+q^{13}+\cdots\)
3744.2.a.bf 3744.a 1.a $4$ $29.896$ \(\Q(\zeta_{20})^+\) None \(0\) \(0\) \(4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{3})q^{5}-\beta _{2}q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3744))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3744)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(288))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(416))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(624))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(936))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1248))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1872))\)\(^{\oplus 2}\)