Properties

Label 48.14.a
Level $48$
Weight $14$
Character orbit 48.a
Rep. character $\chi_{48}(1,\cdot)$
Character field $\Q$
Dimension $13$
Newform subspaces $9$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 48.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(48))\).

Total New Old
Modular forms 110 13 97
Cusp forms 98 13 85
Eisenstein series 12 0 12

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

\(2\)\(3\)FrickeDim
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(7\)

Trace form

\( 13 q + 729 q^{3} - 33802 q^{5} - 182880 q^{7} + 6908733 q^{9} + 4723996 q^{11} - 17021162 q^{13} - 22781250 q^{15} - 49714598 q^{17} - 124175324 q^{19} + 468181576 q^{23} + 3738049763 q^{25} + 387420489 q^{27}+ \cdots + 2510525158236 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(48))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
48.14.a.a 48.a 1.a $1$ $51.471$ \(\Q\) None 12.14.a.b \(0\) \(-729\) \(-24570\) \(173704\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{6}q^{3}-24570q^{5}+173704q^{7}+\cdots\)
48.14.a.b 48.a 1.a $1$ $51.471$ \(\Q\) None 24.14.a.a \(0\) \(-729\) \(-22490\) \(-181272\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3^{6}q^{3}-22490q^{5}-181272q^{7}+\cdots\)
48.14.a.c 48.a 1.a $1$ $51.471$ \(\Q\) None 3.14.a.a \(0\) \(729\) \(-30210\) \(-235088\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{6}q^{3}-30210q^{5}-235088q^{7}+\cdots\)
48.14.a.d 48.a 1.a $1$ $51.471$ \(\Q\) None 12.14.a.a \(0\) \(729\) \(-14850\) \(62896\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{6}q^{3}-14850q^{5}+62896q^{7}+\cdots\)
48.14.a.e 48.a 1.a $1$ $51.471$ \(\Q\) None 6.14.a.a \(0\) \(729\) \(54654\) \(-176336\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3^{6}q^{3}+54654q^{5}-176336q^{7}+\cdots\)
48.14.a.f 48.a 1.a $2$ $51.471$ \(\Q(\sqrt{62869}) \) None 24.14.a.d \(0\) \(-1458\) \(5068\) \(-104880\) $+$ $+$ $\mathrm{SU}(2)$ \(q-3^{6}q^{3}+(2534-\beta )q^{5}+(-52440+\cdots)q^{7}+\cdots\)
48.14.a.g 48.a 1.a $2$ $51.471$ \(\Q(\sqrt{1969}) \) None 3.14.a.b \(0\) \(-1458\) \(40716\) \(21008\) $-$ $+$ $\mathrm{SU}(2)$ \(q-3^{6}q^{3}+(20358-\beta )q^{5}+(10504+\cdots)q^{7}+\cdots\)
48.14.a.h 48.a 1.a $2$ $51.471$ \(\Q(\sqrt{406}) \) None 24.14.a.b \(0\) \(1458\) \(-30916\) \(532896\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3^{6}q^{3}+(-15458+7\beta )q^{5}+(266448+\cdots)q^{7}+\cdots\)
48.14.a.i 48.a 1.a $2$ $51.471$ \(\Q(\sqrt{1621}) \) None 24.14.a.c \(0\) \(1458\) \(-11204\) \(-275808\) $+$ $-$ $\mathrm{SU}(2)$ \(q+3^{6}q^{3}+(-5602-\beta )q^{5}+(-137904+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(48))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(48)) \simeq \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 5}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 3}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)