Properties

Label 288.2.v
Level $288$
Weight $2$
Character orbit 288.v
Rep. character $\chi_{288}(37,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $76$
Newform subspaces $4$
Sturm bound $96$
Trace bound $14$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 288 = 2^{5} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 288.v (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 32 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(14\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(288, [\chi])\).

Total New Old
Modular forms 208 84 124
Cusp forms 176 76 100
Eisenstein series 32 8 24

Trace form

\( 76q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} + O(q^{10}) \) \( 76q + 4q^{2} - 4q^{4} + 4q^{5} - 4q^{7} + 4q^{8} - 12q^{10} + 4q^{11} - 4q^{13} + 20q^{14} - 4q^{19} + 20q^{20} - 24q^{22} + 12q^{23} - 4q^{25} - 16q^{26} - 24q^{28} + 4q^{29} + 16q^{31} - 16q^{32} - 16q^{34} + 28q^{35} - 4q^{37} - 44q^{38} - 56q^{40} + 4q^{41} + 4q^{43} - 44q^{44} - 36q^{46} - 60q^{50} - 12q^{52} + 20q^{53} + 28q^{55} - 64q^{56} - 72q^{58} - 28q^{59} - 36q^{61} - 24q^{62} + 56q^{64} + 8q^{65} - 12q^{67} - 8q^{68} + 80q^{70} - 28q^{71} - 4q^{73} + 20q^{74} + 12q^{76} + 20q^{77} + 64q^{80} + 76q^{82} - 36q^{83} + 16q^{85} + 88q^{86} + 80q^{88} + 4q^{89} - 52q^{91} + 120q^{92} + 56q^{94} - 56q^{95} - 8q^{97} + 104q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(288, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
288.2.v.a \(4\) \(2.300\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(4\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(1+\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
288.2.v.b \(8\) \(2.300\) 8.0.18939904.2 None \(4\) \(0\) \(0\) \(-8\) \(q+\beta _{2}q^{2}+(\beta _{2}-\beta _{3}+\beta _{6})q^{4}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)
288.2.v.c \(32\) \(2.300\) None \(0\) \(0\) \(0\) \(0\)
288.2.v.d \(32\) \(2.300\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(32, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 2}\)