Properties

Label 315.2.d
Level $315$
Weight $2$
Character orbit 315.d
Rep. character $\chi_{315}(64,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $5$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(11\), \(29\)

Dimensions

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

Total New Old
Modular forms 56 14 42
Cusp forms 40 14 26
Eisenstein series 16 0 16

Trace form

\( 14q - 8q^{4} + O(q^{10}) \) \( 14q - 8q^{4} - 8q^{10} + 6q^{11} - 4q^{14} + 12q^{16} + 20q^{20} + 10q^{25} - 28q^{26} - 10q^{29} - 28q^{31} - 4q^{34} - 2q^{35} + 4q^{40} - 12q^{41} + 20q^{44} + 8q^{46} - 14q^{49} + 24q^{50} + 4q^{55} + 24q^{56} + 36q^{59} + 8q^{61} - 52q^{64} - 22q^{65} + 8q^{70} - 16q^{71} - 72q^{74} + 16q^{76} + 10q^{79} - 60q^{80} + 22q^{85} + 16q^{86} + 40q^{89} - 2q^{91} + 92q^{94} - 16q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.2.d.a \(2\) \(2.515\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+2iq^{2}-2q^{4}+(2-i)q^{5}+iq^{7}+\cdots\)
315.2.d.b \(2\) \(2.515\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+iq^{2}+q^{4}+(-2+i)q^{5}+iq^{7}+\cdots\)
315.2.d.c \(2\) \(2.515\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+iq^{2}+q^{4}+(-1-2i)q^{5}-iq^{7}+\cdots\)
315.2.d.d \(2\) \(2.515\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) \(q+iq^{2}+q^{4}+(2+i)q^{5}-iq^{7}+3iq^{8}+\cdots\)
315.2.d.e \(6\) \(2.515\) 6.0.350464.1 None \(0\) \(0\) \(-2\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)