Properties

Label 312.2.bp
Level $312$
Weight $2$
Character orbit 312.bp
Rep. character $\chi_{312}(41,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $56$
Newform subspaces $1$
Sturm bound $112$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 312.bp (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Newform subspaces: \( 1 \)
Sturm bound: \(112\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(312, [\chi])\).

Total New Old
Modular forms 256 56 200
Cusp forms 192 56 136
Eisenstein series 64 0 64

Trace form

\( 56q + 4q^{7} + O(q^{10}) \) \( 56q + 4q^{7} + 8q^{13} - 8q^{15} + 4q^{19} + 16q^{21} + 24q^{27} - 36q^{31} + 28q^{33} + 20q^{37} + 16q^{39} - 84q^{43} + 12q^{45} - 12q^{49} - 24q^{55} - 36q^{57} - 24q^{61} - 12q^{63} - 32q^{67} - 36q^{69} - 20q^{73} - 60q^{75} - 32q^{79} - 88q^{85} - 16q^{87} + 28q^{91} - 88q^{93} - 36q^{97} + 44q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(312, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
312.2.bp.a \(56\) \(2.491\) None \(0\) \(0\) \(0\) \(4\)

Decomposition of \(S_{2}^{\mathrm{old}}(312, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(78, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(156, [\chi])\)\(^{\oplus 2}\)