Properties

Label 315.5.e
Level $315$
Weight $5$
Character orbit 315.e
Rep. character $\chi_{315}(244,\cdot)$
Character field $\Q$
Dimension $78$
Newform subspaces $7$
Sturm bound $240$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 315.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(240\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(315, [\chi])\).

Total New Old
Modular forms 200 82 118
Cusp forms 184 78 106
Eisenstein series 16 4 12

Trace form

\( 78 q - 612 q^{4} + O(q^{10}) \) \( 78 q - 612 q^{4} - 2 q^{11} - 228 q^{14} + 5220 q^{16} - 846 q^{25} + 742 q^{29} + 1454 q^{35} - 3944 q^{44} + 6504 q^{46} - 1638 q^{49} - 1404 q^{50} + 13968 q^{56} - 20868 q^{64} + 2314 q^{65} + 4236 q^{70} + 9148 q^{71} - 10152 q^{74} - 14190 q^{79} + 18450 q^{85} - 74712 q^{86} - 55302 q^{91} + 31068 q^{95} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
315.5.e.a \(1\) \(32.562\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(-25\) \(49\) \(q+2^{4}q^{4}-5^{2}q^{5}+7^{2}q^{7}+73q^{11}+\cdots\)
315.5.e.b \(1\) \(32.562\) \(\Q\) \(\Q(\sqrt{-35}) \) \(0\) \(0\) \(25\) \(-49\) \(q+2^{4}q^{4}+5^{2}q^{5}-7^{2}q^{7}+73q^{11}+\cdots\)
315.5.e.c \(2\) \(32.562\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(-10\) \(70\) \(q+\beta q^{2}+10q^{4}+(-5-10\beta )q^{5}+(35+\cdots)q^{7}+\cdots\)
315.5.e.d \(2\) \(32.562\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(10\) \(-70\) \(q+\beta q^{2}+10q^{4}+(5+10\beta )q^{5}+(-35+\cdots)q^{7}+\cdots\)
315.5.e.e \(8\) \(32.562\) \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-22+\beta _{2})q^{4}+(-\beta _{1}-\beta _{7})q^{5}+\cdots\)
315.5.e.f \(32\) \(32.562\) None \(0\) \(0\) \(0\) \(0\)
315.5.e.g \(32\) \(32.562\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{5}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(315, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)