Properties

Label 405.4.b
Level $405$
Weight $4$
Character orbit 405.b
Rep. character $\chi_{405}(244,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $6$
Sturm bound $216$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(216\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(405, [\chi])\).

Total New Old
Modular forms 174 76 98
Cusp forms 150 68 82
Eisenstein series 24 8 16

Trace form

\( 68 q - 252 q^{4} + O(q^{10}) \) \( 68 q - 252 q^{4} - 56 q^{10} + 868 q^{16} - 8 q^{19} + 92 q^{25} + 76 q^{31} - 424 q^{34} + 344 q^{40} - 508 q^{46} - 1180 q^{49} + 1182 q^{55} + 1444 q^{61} - 3028 q^{64} + 1356 q^{70} - 2232 q^{76} + 1444 q^{79} - 410 q^{85} + 204 q^{91} - 6340 q^{94} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(405, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
405.4.b.a \(4\) \(23.896\) \(\Q(\sqrt{3}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-2\beta _{1}-\beta _{2})q^{2}-9q^{4}+5\beta _{1}q^{5}+\cdots\)
405.4.b.b \(8\) \(23.896\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(-15\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+(-2+\beta _{4}+\cdots)q^{5}+\cdots\)
405.4.b.c \(8\) \(23.896\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(15\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+(2-\beta _{3})q^{5}+\cdots\)
405.4.b.d \(16\) \(23.896\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{4}q^{2}+(-4-\beta _{1})q^{4}+(-\beta _{4}+\beta _{11}+\cdots)q^{5}+\cdots\)
405.4.b.e \(16\) \(23.896\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-3\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+\beta _{9}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
405.4.b.f \(16\) \(23.896\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(3\) \(0\) \(q+\beta _{1}q^{2}+(-3+\beta _{2})q^{4}+\beta _{8}q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(405, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(405, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)