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Properties

Label 2352.3.bn
Level $2352$
Weight $3$
Character orbit 2352.bn
Rep. character $\chi_{2352}(1745,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $312$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2352.bn (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(2352, [\chi])\).

Total New Old
Modular forms 1888 328 1560
Cusp forms 1696 312 1384
Eisenstein series 192 16 176

Trace form

\( 312 q - q^{3} + q^{9} + O(q^{10}) \) \( 312 q - q^{3} + q^{9} + 8 q^{13} - 10 q^{15} + 14 q^{19} + 694 q^{25} - 4 q^{27} - 58 q^{31} + 19 q^{33} + 2 q^{37} - 106 q^{39} - 208 q^{43} + 11 q^{45} + 187 q^{51} - 108 q^{55} + 38 q^{57} + 2 q^{61} - 162 q^{67} + 214 q^{69} + 74 q^{73} - 102 q^{75} + 198 q^{79} + 153 q^{81} + 20 q^{85} + 80 q^{87} - 43 q^{93} + 216 q^{97} + 902 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)