Properties

Label 315.2.be
Level 315
Weight 2
Character orbit be
Rep. character \(\chi_{315}(236,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 64
Newforms 3
Sturm bound 96
Trace bound 1

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Defining parameters

Level: \( N \) = \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 315.be (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 3 \)
Sturm bound: \(96\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

Total New Old
Modular forms 104 64 40
Cusp forms 88 64 24
Eisenstein series 16 0 16

Trace form

\(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(64q \) \(\mathstrut +\mathstrut 32q^{4} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 4q^{9} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 32q^{16} \) \(\mathstrut +\mathstrut 28q^{18} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 18q^{24} \) \(\mathstrut +\mathstrut 64q^{25} \) \(\mathstrut -\mathstrut 24q^{26} \) \(\mathstrut -\mathstrut 18q^{27} \) \(\mathstrut -\mathstrut 8q^{28} \) \(\mathstrut +\mathstrut 18q^{29} \) \(\mathstrut -\mathstrut 4q^{30} \) \(\mathstrut +\mathstrut 24q^{31} \) \(\mathstrut -\mathstrut 24q^{33} \) \(\mathstrut +\mathstrut 36q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 120q^{38} \) \(\mathstrut -\mathstrut 36q^{39} \) \(\mathstrut +\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut -\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut +\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 36q^{47} \) \(\mathstrut +\mathstrut 60q^{48} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut +\mathstrut 102q^{56} \) \(\mathstrut +\mathstrut 6q^{57} \) \(\mathstrut +\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 30q^{60} \) \(\mathstrut -\mathstrut 60q^{61} \) \(\mathstrut +\mathstrut 14q^{63} \) \(\mathstrut -\mathstrut 64q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 48q^{66} \) \(\mathstrut +\mathstrut 14q^{67} \) \(\mathstrut -\mathstrut 60q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 76q^{72} \) \(\mathstrut -\mathstrut 54q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 4q^{79} \) \(\mathstrut +\mathstrut 44q^{81} \) \(\mathstrut +\mathstrut 60q^{83} \) \(\mathstrut -\mathstrut 54q^{84} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 102q^{87} \) \(\mathstrut -\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 54q^{90} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 60q^{93} \) \(\mathstrut +\mathstrut 60q^{96} \) \(\mathstrut -\mathstrut 6q^{97} \) \(\mathstrut -\mathstrut 54q^{98} \) \(\mathstrut -\mathstrut 2q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.be.a \(2\) \(2.515\) \(\Q(\sqrt{-3}) \) None \(-3\) \(0\) \(2\) \(-5\) \(q+(-1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
315.2.be.b \(30\) \(2.515\) None \(3\) \(-1\) \(30\) \(6\)
315.2.be.c \(32\) \(2.515\) None \(0\) \(1\) \(-32\) \(1\)

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)