Properties

Label 10.16.a
Level $10$
Weight $16$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $24$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 16 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_0(10))\).

Total New Old
Modular forms 25 5 20
Cusp forms 21 5 16
Eisenstein series 4 0 4

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

\(2\)\(5\)FrickeDim
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\( 5 q + 128 q^{2} - 9632 q^{3} + 81920 q^{4} + 78125 q^{5} + 427520 q^{6} + 535804 q^{7} + 2097152 q^{8} + 11409985 q^{9} + 10000000 q^{10} - 21143940 q^{11} - 157810688 q^{12} + 744201478 q^{13} - 343946240 q^{14}+ \cdots + 15\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_0(10))\) 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 5
10.16.a.a 10.a 1.a $1$ $14.269$ \(\Q\) None 10.16.a.a \(-128\) \(-5568\) \(78125\) \(2564996\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}-5568q^{3}+2^{14}q^{4}+5^{7}q^{5}+\cdots\)
10.16.a.b 10.a 1.a $1$ $14.269$ \(\Q\) None 10.16.a.b \(-128\) \(-918\) \(-78125\) \(-953554\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{7}q^{2}-918q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.c 10.a 1.a $1$ $14.269$ \(\Q\) None 10.16.a.c \(128\) \(-1302\) \(-78125\) \(-90706\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{7}q^{2}-1302q^{3}+2^{14}q^{4}-5^{7}q^{5}+\cdots\)
10.16.a.d 10.a 1.a $2$ $14.269$ \(\Q(\sqrt{239569}) \) None 10.16.a.d \(256\) \(-1844\) \(156250\) \(-984932\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{7}q^{2}+(-922-\beta )q^{3}+2^{14}q^{4}+\cdots\)

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{16}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)