Properties

Label 448.2.a
Level $448$
Weight $2$
Character orbit 448.a
Rep. character $\chi_{448}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $10$
Sturm bound $128$
Trace bound $7$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 448.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(448))\).

Total New Old
Modular forms 76 12 64
Cusp forms 53 12 41
Eisenstein series 23 0 23

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.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(4\)
\(-\)\(+\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(7\)

Trace form

\( 12 q + 12 q^{9} + O(q^{10}) \) \( 12 q + 12 q^{9} - 8 q^{17} + 4 q^{25} - 8 q^{29} - 16 q^{33} - 8 q^{37} - 24 q^{41} + 48 q^{45} + 12 q^{49} + 40 q^{53} - 16 q^{57} - 32 q^{61} + 16 q^{69} + 8 q^{73} - 8 q^{77} - 4 q^{81} - 32 q^{85} + 8 q^{89} - 8 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(448))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 7
448.2.a.a 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
448.2.a.b 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(-2\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
448.2.a.c 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(-2\) \(4\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}+q^{7}+q^{9}-8q^{15}+\cdots\)
448.2.a.d 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(0\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-q^{7}-3q^{9}+4q^{11}-2q^{13}+\cdots\)
448.2.a.e 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(0\) \(-2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
448.2.a.f 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(2\) \(0\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
448.2.a.g 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(2\) \(0\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+4q^{13}+6q^{17}+\cdots\)
448.2.a.h 448.a 1.a $1$ $3.577$ \(\Q\) None \(0\) \(2\) \(4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}-q^{7}+q^{9}+8q^{15}+\cdots\)
448.2.a.i 448.a 1.a $2$ $3.577$ \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(-2\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
448.2.a.j 448.a 1.a $2$ $3.577$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-2\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(448))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(448)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 2}\)