Properties

Label 224.2.a
Level $224$
Weight $2$
Character orbit 224.a
Rep. character $\chi_{224}(1,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $4$
Sturm bound $64$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 224.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(64\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(224))\).

Total New Old
Modular forms 40 6 34
Cusp forms 25 6 19
Eisenstein series 15 0 15

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

Trace form

\( 6 q + 4 q^{5} + 14 q^{9} + O(q^{10}) \) \( 6 q + 4 q^{5} + 14 q^{9} + 4 q^{13} - 4 q^{17} - 6 q^{25} + 4 q^{29} - 16 q^{33} + 20 q^{37} - 36 q^{41} - 28 q^{45} + 6 q^{49} - 44 q^{53} + 20 q^{61} - 8 q^{65} - 48 q^{69} + 12 q^{73} + 22 q^{81} + 40 q^{85} + 12 q^{89} - 32 q^{93} + 28 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(224))\) 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
224.2.a.a 224.a 1.a $1$ $1.789$ \(\Q\) None 224.2.a.a \(0\) \(-2\) \(0\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
224.2.a.b 224.a 1.a $1$ $1.789$ \(\Q\) None 224.2.a.a \(0\) \(2\) \(0\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
224.2.a.c 224.a 1.a $2$ $1.789$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(-2\) \(2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
224.2.a.d 224.a 1.a $2$ $1.789$ \(\Q(\sqrt{5}) \) None 224.2.a.c \(0\) \(2\) \(2\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(224))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(224)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)