Properties

Label 312.2.m
Level $312$
Weight $2$
Character orbit 312.m
Rep. character $\chi_{312}(181,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $3$
Sturm bound $112$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 312 = 2^{3} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 312.m (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 104 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(112\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 60 28 32
Cusp forms 52 28 24
Eisenstein series 8 0 8

Trace form

\( 28 q - 28 q^{9} + O(q^{10}) \) \( 28 q - 28 q^{9} + 4 q^{10} - 4 q^{12} + 16 q^{14} + 12 q^{16} + 8 q^{17} - 28 q^{22} + 36 q^{25} - 12 q^{26} - 4 q^{30} + 40 q^{38} - 4 q^{40} - 32 q^{42} - 16 q^{48} - 44 q^{49} + 4 q^{52} + 48 q^{55} - 32 q^{56} - 88 q^{62} + 24 q^{64} - 24 q^{65} + 12 q^{66} - 8 q^{68} - 4 q^{78} - 40 q^{79} + 28 q^{81} + 76 q^{82} + 24 q^{87} - 44 q^{88} - 4 q^{90} - 40 q^{92} + 76 q^{94} - 80 q^{95} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
312.2.m.a 312.m 104.e $2$ $2.491$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}-2q^{5}+\cdots\)
312.2.m.b 312.m 104.e $2$ $2.491$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+2q^{5}+\cdots\)
312.2.m.c 312.m 104.e $24$ $2.491$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(312, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 2}\)