Properties

Label 624.2.a
Level $624$
Weight $2$
Character orbit 624.a
Rep. character $\chi_{624}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $11$
Sturm bound $224$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(224\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(624))\).

Total New Old
Modular forms 124 12 112
Cusp forms 101 12 89
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.

\(2\)\(3\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(1\)
\(-\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(4\)
Minus space\(-\)\(8\)

Trace form

\( 12q + 4q^{7} + 12q^{9} + O(q^{10}) \) \( 12q + 4q^{7} + 12q^{9} + 8q^{11} + 4q^{15} - 4q^{19} - 16q^{23} + 20q^{25} - 16q^{29} + 20q^{31} + 8q^{33} - 16q^{37} + 4q^{39} + 16q^{43} + 24q^{47} + 20q^{49} + 8q^{51} - 8q^{53} - 16q^{55} - 8q^{61} + 4q^{63} + 20q^{67} - 16q^{69} - 16q^{71} + 8q^{73} + 8q^{75} - 8q^{77} + 16q^{79} + 12q^{81} - 48q^{83} - 12q^{91} + 16q^{93} - 8q^{97} + 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(624))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 13
624.2.a.a \(1\) \(4.983\) \(\Q\) None \(0\) \(-1\) \(-4\) \(4\) \(+\) \(+\) \(+\) \(q-q^{3}-4q^{5}+4q^{7}+q^{9}+2q^{11}+\cdots\)
624.2.a.b \(1\) \(4.983\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q-q^{3}-2q^{7}+q^{9}+q^{13}-6q^{17}+\cdots\)
624.2.a.c \(1\) \(4.983\) \(\Q\) None \(0\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{3}+q^{9}-6q^{11}-q^{13}+2q^{17}+\cdots\)
624.2.a.d \(1\) \(4.983\) \(\Q\) None \(0\) \(-1\) \(2\) \(0\) \(+\) \(+\) \(-\) \(q-q^{3}+2q^{5}+q^{9}+q^{13}-2q^{15}+\cdots\)
624.2.a.e \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(-4\) \(2\) \(-\) \(-\) \(-\) \(q+q^{3}-4q^{5}+2q^{7}+q^{9}+4q^{11}+\cdots\)
624.2.a.f \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(-2\) \(-4\) \(+\) \(-\) \(-\) \(q+q^{3}-2q^{5}-4q^{7}+q^{9}+q^{13}-2q^{15}+\cdots\)
624.2.a.g \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{7}+q^{9}+2q^{11}-q^{13}+\cdots\)
624.2.a.h \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(2\) \(-4\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
624.2.a.i \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(2\) \(4\) \(-\) \(-\) \(-\) \(q+q^{3}+2q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
624.2.a.j \(1\) \(4.983\) \(\Q\) None \(0\) \(1\) \(4\) \(0\) \(+\) \(-\) \(+\) \(q+q^{3}+4q^{5}+q^{9}+2q^{11}-q^{13}+\cdots\)
624.2.a.k \(2\) \(4.983\) \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-q^{3}+\beta q^{5}+\beta q^{7}+q^{9}+2q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(624))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(208))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)