Properties

Label 252.4.a
Level $252$
Weight $4$
Character orbit 252.a
Rep. character $\chi_{252}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $6$
Sturm bound $192$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(192\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(252))\).

Total New Old
Modular forms 156 8 148
Cusp forms 132 8 124
Eisenstein series 24 0 24

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

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

Trace form

\( 8q - 18q^{5} + O(q^{10}) \) \( 8q - 18q^{5} + 12q^{11} + 14q^{13} - 12q^{17} + 46q^{19} + 24q^{23} - 108q^{25} - 132q^{29} - 52q^{31} - 42q^{35} + 316q^{37} + 252q^{41} - 740q^{43} + 924q^{47} + 392q^{49} - 312q^{53} + 296q^{55} - 846q^{59} - 934q^{61} - 732q^{65} + 696q^{67} + 456q^{71} + 648q^{73} - 420q^{77} + 632q^{79} - 390q^{83} - 460q^{85} + 2232q^{89} + 350q^{91} - 1032q^{95} - 204q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(252))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 7
252.4.a.a \(1\) \(14.868\) \(\Q\) None \(0\) \(0\) \(-14\) \(-7\) \(-\) \(-\) \(+\) \(q-14q^{5}-7q^{7}-4q^{11}+54q^{13}+\cdots\)
252.4.a.b \(1\) \(14.868\) \(\Q\) None \(0\) \(0\) \(-6\) \(7\) \(-\) \(-\) \(-\) \(q-6q^{5}+7q^{7}-6^{2}q^{11}+62q^{13}+\cdots\)
252.4.a.c \(1\) \(14.868\) \(\Q\) None \(0\) \(0\) \(-6\) \(7\) \(-\) \(-\) \(-\) \(q-6q^{5}+7q^{7}+12q^{11}-82q^{13}+\cdots\)
252.4.a.d \(1\) \(14.868\) \(\Q\) None \(0\) \(0\) \(8\) \(-7\) \(-\) \(-\) \(+\) \(q+8q^{5}-7q^{7}+40q^{11}-12q^{13}+\cdots\)
252.4.a.e \(2\) \(14.868\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(-14\) \(-\) \(+\) \(+\) \(q+\beta q^{5}-7q^{7}-13\beta q^{11}-30q^{13}+\cdots\)
252.4.a.f \(2\) \(14.868\) \(\Q(\sqrt{7}) \) None \(0\) \(0\) \(0\) \(14\) \(-\) \(+\) \(-\) \(q+\beta q^{5}+7q^{7}+\beta q^{11}+26q^{13}-5\beta q^{17}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(252))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(252)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)