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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(224))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
224.2.a.a \(1\) \(1.789\) \(\Q\) None \(0\) \(-2\) \(0\) \(-1\) \(+\) \(+\) \(q-2q^{3}-q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
224.2.a.b \(1\) \(1.789\) \(\Q\) None \(0\) \(2\) \(0\) \(1\) \(+\) \(-\) \(q+2q^{3}+q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
224.2.a.c \(2\) \(1.789\) \(\Q(\sqrt{5}) \) None \(0\) \(-2\) \(2\) \(2\) \(+\) \(-\) \(q+(-1-\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
224.2.a.d \(2\) \(1.789\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(2\) \(-2\) \(-\) \(+\) \(q+(1+\beta )q^{3}+(1-\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)

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

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