Properties

Label 147.4.c
Level $147$
Weight $4$
Character orbit 147.c
Rep. character $\chi_{147}(146,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $74$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 147.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(147, [\chi])\).

Total New Old
Modular forms 64 44 20
Cusp forms 48 36 12
Eisenstein series 16 8 8

Trace form

\( 36 q - 124 q^{4} - 58 q^{9} + O(q^{10}) \) \( 36 q - 124 q^{4} - 58 q^{9} + 262 q^{15} + 596 q^{16} - 164 q^{18} - 652 q^{22} + 828 q^{25} - 60 q^{30} + 1436 q^{36} - 1096 q^{37} - 1516 q^{39} - 1636 q^{43} + 2528 q^{46} + 522 q^{51} + 2302 q^{57} + 644 q^{58} - 3996 q^{60} - 4052 q^{64} + 2208 q^{67} - 2048 q^{72} + 6544 q^{78} - 564 q^{79} - 3642 q^{81} - 3396 q^{85} + 484 q^{88} - 274 q^{93} - 2034 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
147.4.c.a \(12\) \(8.673\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(-2+\beta _{11})q^{4}+\cdots\)
147.4.c.b \(24\) \(8.673\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{4}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(147, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)