↑

Properties

Label 3234.2.br
Level $3234$
Weight $2$
Character orbit 3234.br
Rep. character $\chi_{3234}(241,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1344$
Sturm bound $1344$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3234.br (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 539 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3234, [\chi])\).

Total New Old
Modular forms 8160 1344 6816
Cusp forms 7968 1344 6624
Eisenstein series 192 0 192

Trace form

\( 1344 q - 112 q^{4} - 24 q^{5} - 112 q^{9} + O(q^{10}) \) \( 1344 q - 112 q^{4} - 24 q^{5} - 112 q^{9} + 36 q^{11} - 16 q^{14} - 20 q^{15} + 112 q^{16} + 56 q^{20} + 18 q^{22} + 8 q^{23} - 108 q^{25} + 32 q^{26} - 12 q^{31} - 6 q^{33} - 224 q^{36} - 20 q^{37} - 88 q^{38} + 44 q^{42} + 48 q^{44} + 88 q^{45} - 232 q^{47} - 212 q^{49} + 112 q^{53} - 42 q^{55} + 104 q^{56} - 84 q^{58} - 56 q^{59} - 52 q^{60} + 224 q^{64} + 88 q^{70} + 48 q^{71} + 24 q^{75} - 64 q^{77} + 24 q^{80} + 112 q^{81} + 24 q^{82} + 192 q^{86} + 30 q^{88} - 320 q^{89} + 72 q^{91} + 16 q^{92} - 16 q^{93} + 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3234, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3234, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3234, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(539, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1078, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1617, [\chi])\)\(^{\oplus 2}\)