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Properties

Label 2352.2.dg
Level $2352$
Weight $2$
Character orbit 2352.dg
Rep. character $\chi_{2352}(17,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1320$
Sturm bound $896$

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Defining parameters

Level: \( N \) \(=\) \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2352.dg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2352, [\chi])\).

Total New Old
Modular forms 5520 1368 4152
Cusp forms 5232 1320 3912
Eisenstein series 288 48 240

Trace form

\( 1320 q + 11 q^{3} + 26 q^{7} - 13 q^{9} + O(q^{10}) \) \( 1320 q + 11 q^{3} + 26 q^{7} - 13 q^{9} - 28 q^{13} + 16 q^{15} + 30 q^{19} - 13 q^{21} + 80 q^{25} + 14 q^{27} - 6 q^{31} - 11 q^{33} - 26 q^{37} + 16 q^{39} + 48 q^{43} + q^{45} - 24 q^{49} + 29 q^{51} + 28 q^{55} - 25 q^{57} - 22 q^{61} + 21 q^{63} + 14 q^{67} - 70 q^{69} - 10 q^{73} - 46 q^{75} + 26 q^{79} + 19 q^{81} - 40 q^{85} + 74 q^{87} + 166 q^{91} - 36 q^{93} - 30 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2352, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2352, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2352, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1176, [\chi])\)\(^{\oplus 2}\)