Properties

Label 14.10.a
Level $14$
Weight $10$
Character orbit 14.a
Rep. character $\chi_{14}(1,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $3$
Sturm bound $20$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 14.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(14))\).

Total New Old
Modular forms 20 4 16
Cusp forms 16 4 12
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.

\(2\)\(7\)FrickeDim
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(1\)
Minus space\(-\)\(3\)

Trace form

\( 4 q - 32 q^{2} + 150 q^{3} + 1024 q^{4} - 1626 q^{5} + 3040 q^{6} - 8192 q^{8} + 65552 q^{9} + 43424 q^{10} + 39612 q^{11} + 38400 q^{12} - 28766 q^{13} - 76832 q^{14} + 592280 q^{15} + 262144 q^{16} - 885564 q^{17}+ \cdots + 2882415692 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(14))\) 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 7
14.10.a.a 14.a 1.a $1$ $7.211$ \(\Q\) None 14.10.a.a \(-16\) \(-6\) \(560\) \(-2401\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}-6q^{3}+2^{8}q^{4}+560q^{5}+\cdots\)
14.10.a.b 14.a 1.a $1$ $7.211$ \(\Q\) None 14.10.a.b \(16\) \(170\) \(544\) \(-2401\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+170q^{3}+2^{8}q^{4}+544q^{5}+\cdots\)
14.10.a.c 14.a 1.a $2$ $7.211$ \(\Q(\sqrt{2305}) \) None 14.10.a.c \(-32\) \(-14\) \(-2730\) \(4802\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(-7-5\beta )q^{3}+2^{8}q^{4}+(-1365+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(14)) \simeq \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)