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Properties

Label 2352.3.db
Level $2352$
Weight $3$
Character orbit 2352.db
Rep. character $\chi_{2352}(145,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
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.db (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

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

Total New Old
Modular forms 10896 1344 9552
Cusp forms 10608 1344 9264
Eisenstein series 288 0 288

Trace form

\( 1344 q + 8 q^{7} - 336 q^{9} + O(q^{10}) \) \( 1344 q + 8 q^{7} - 336 q^{9} + 48 q^{19} + 48 q^{23} - 568 q^{25} - 24 q^{31} + 72 q^{33} - 240 q^{35} - 192 q^{39} - 32 q^{43} - 288 q^{47} - 48 q^{49} - 16 q^{53} + 48 q^{57} + 192 q^{59} + 144 q^{61} + 144 q^{63} + 80 q^{65} + 176 q^{67} - 640 q^{71} + 120 q^{73} + 80 q^{77} + 56 q^{79} + 1008 q^{81} + 288 q^{91} - 192 q^{95} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(784, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)