Properties

Label 10.20.a
Level $10$
Weight $20$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $30$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_0(10))\).

Total New Old
Modular forms 31 5 26
Cusp forms 27 5 22
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

\( 5 q + 512 q^{2} + 70372 q^{3} + 1310720 q^{4} + 1953125 q^{5} + 23736320 q^{6} - 272909624 q^{7} + 134217728 q^{8} - 93890015 q^{9} + 1000000000 q^{10} - 23642432940 q^{11} + 18447597568 q^{12} + 42687059302 q^{13}+ \cdots + 26\!\cdots\!20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_0(10))\) 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
10.20.a.a 10.a 1.a $1$ $22.882$ \(\Q\) None 10.20.a.a \(-512\) \(-26622\) \(-1953125\) \(-39884026\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{9}q^{2}-26622q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)
10.20.a.b 10.a 1.a $1$ $22.882$ \(\Q\) None 10.20.a.b \(-512\) \(38628\) \(1953125\) \(-144185776\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{9}q^{2}+38628q^{3}+2^{18}q^{4}+5^{9}q^{5}+\cdots\)
10.20.a.c 10.a 1.a $1$ $22.882$ \(\Q\) None 10.20.a.c \(512\) \(24642\) \(-1953125\) \(-171901114\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{9}q^{2}+24642q^{3}+2^{18}q^{4}-5^{9}q^{5}+\cdots\)
10.20.a.d 10.a 1.a $2$ $22.882$ \(\mathbb{Q}[x]/(x^{2} - \cdots)\) None 10.20.a.d \(1024\) \(33724\) \(3906250\) \(83061292\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{9}q^{2}+(16862-\beta )q^{3}+2^{18}q^{4}+\cdots\)

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{20}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{20}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)