Properties

Label 10.12.a
Level $10$
Weight $12$
Character orbit 10.a
Rep. character $\chi_{10}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $18$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 10.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(10))\).

Total New Old
Modular forms 19 5 14
Cusp forms 15 5 10
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

\( 5 q + 32 q^{2} + 1012 q^{3} + 5120 q^{4} + 3125 q^{5} - 14080 q^{6} - 45224 q^{7} + 32768 q^{8} + 336385 q^{9} + 100000 q^{10} + 672660 q^{11} + 1036288 q^{12} - 2191418 q^{13} - 2176640 q^{14} + 537500 q^{15}+ \cdots + 146930040420 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(10))\) 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
10.12.a.a 10.a 1.a $1$ $7.683$ \(\Q\) None 10.12.a.a \(-32\) \(-12\) \(3125\) \(-14176\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}-12q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)
10.12.a.b 10.a 1.a $1$ $7.683$ \(\Q\) None 10.12.a.b \(-32\) \(738\) \(-3125\) \(25574\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+738q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.c 10.a 1.a $1$ $7.683$ \(\Q\) None 10.12.a.c \(32\) \(-318\) \(-3125\) \(-70714\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}-318q^{3}+2^{10}q^{4}-5^{5}q^{5}+\cdots\)
10.12.a.d 10.a 1.a $2$ $7.683$ \(\Q(\sqrt{1969}) \) None 10.12.a.d \(64\) \(604\) \(6250\) \(14092\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(302-\beta )q^{3}+2^{10}q^{4}+5^{5}q^{5}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(10))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(10)) \simeq \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)