Properties

Label 3969.2.c
Level $3969$
Weight $2$
Character orbit 3969.c
Rep. character $\chi_{3969}(3968,\cdot)$
Character field $\Q$
Dimension $152$
Sturm bound $1008$

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Defining parameters

Level: \( N \) \(=\) \( 3969 = 3^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3969.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(1008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3969, [\chi])\).

Total New Old
Modular forms 552 168 384
Cusp forms 456 152 304
Eisenstein series 96 16 80

Trace form

\( 152 q - 148 q^{4} + O(q^{10}) \) \( 152 q - 148 q^{4} + 108 q^{16} - 32 q^{22} + 116 q^{25} + 12 q^{37} + 48 q^{43} + 40 q^{46} - 20 q^{58} - 72 q^{64} - 32 q^{67} + 88 q^{79} - 12 q^{85} + 68 q^{88} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3969, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3969, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3969, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(441, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(567, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1323, [\chi])\)\(^{\oplus 2}\)