Properties

Label 224.4.a
Level $224$
Weight $4$
Character orbit 224.a
Rep. character $\chi_{224}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $8$
Sturm bound $128$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 224.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(128\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(224))\).

Total New Old
Modular forms 104 18 86
Cusp forms 88 18 70
Eisenstein series 16 0 16

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.
\(+\)\(+\)\(+\)\(5\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(11\)
Minus space\(-\)\(7\)

Trace form

\( 18q - 4q^{5} + 122q^{9} + O(q^{10}) \) \( 18q - 4q^{5} + 122q^{9} + 92q^{13} + 308q^{17} + 318q^{25} + 284q^{29} + 1232q^{33} - 660q^{37} - 588q^{41} + 1788q^{45} + 882q^{49} + 1388q^{53} - 768q^{57} + 780q^{61} - 1304q^{65} - 1488q^{69} - 1212q^{73} - 2078q^{81} + 1880q^{85} + 388q^{89} - 5856q^{93} - 3628q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(224))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 7
224.4.a.a \(1\) \(13.216\) \(\Q\) None \(0\) \(-2\) \(0\) \(7\) \(+\) \(-\) \(q-2q^{3}+7q^{7}-23q^{9}+20q^{11}-20q^{13}+\cdots\)
224.4.a.b \(1\) \(13.216\) \(\Q\) None \(0\) \(2\) \(0\) \(-7\) \(-\) \(+\) \(q+2q^{3}-7q^{7}-23q^{9}-20q^{11}-20q^{13}+\cdots\)
224.4.a.c \(2\) \(13.216\) \(\Q(\sqrt{37}) \) None \(0\) \(-6\) \(-6\) \(14\) \(+\) \(-\) \(q+(-3-\beta )q^{3}+(-3+\beta )q^{5}+7q^{7}+\cdots\)
224.4.a.d \(2\) \(13.216\) \(\Q(\sqrt{37}) \) None \(0\) \(6\) \(-6\) \(-14\) \(+\) \(+\) \(q+(3+\beta )q^{3}+(-3+\beta )q^{5}-7q^{7}+(19+\cdots)q^{9}+\cdots\)
224.4.a.e \(3\) \(13.216\) 3.3.2981.1 None \(0\) \(-8\) \(10\) \(-21\) \(+\) \(+\) \(q+(-3-\beta _{1})q^{3}+(3+\beta _{2})q^{5}-7q^{7}+\cdots\)
224.4.a.f \(3\) \(13.216\) 3.3.621.1 None \(0\) \(0\) \(-6\) \(-21\) \(-\) \(+\) \(q+\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}-7q^{7}+\cdots\)
224.4.a.g \(3\) \(13.216\) 3.3.621.1 None \(0\) \(0\) \(-6\) \(21\) \(-\) \(-\) \(q-\beta _{1}q^{3}+(-2-2\beta _{1}-\beta _{2})q^{5}+7q^{7}+\cdots\)
224.4.a.h \(3\) \(13.216\) 3.3.2981.1 None \(0\) \(8\) \(10\) \(21\) \(-\) \(-\) \(q+(3+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+7q^{7}+(11+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(224))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(224)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 2}\)