Properties

Label 252.4.f
Level $252$
Weight $4$
Character orbit 252.f
Rep. character $\chi_{252}(125,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(252, [\chi])\).

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

Trace form

\( 8q + 16q^{7} + O(q^{10}) \) \( 8q + 16q^{7} - 40q^{25} + 512q^{37} + 32q^{43} + 632q^{49} - 2336q^{67} + 1792q^{79} - 1344q^{85} + 2496q^{91} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(252, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
252.4.f.a \(8\) \(14.868\) 8.0.\(\cdots\).9 None \(0\) \(0\) \(0\) \(16\) \(q+\beta _{3}q^{5}+(2-\beta _{2})q^{7}-\beta _{5}q^{11}+(\beta _{2}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(252, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(252, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)