Properties

Label 975.2.w
Level $975$
Weight $2$
Character orbit 975.w
Rep. character $\chi_{975}(49,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $11$
Sturm bound $280$
Trace bound $13$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
Sturm bound: \(280\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

Total New Old
Modular forms 304 80 224
Cusp forms 256 80 176
Eisenstein series 48 0 48

Trace form

\( 80q - 36q^{4} + 40q^{9} + O(q^{10}) \) \( 80q - 36q^{4} + 40q^{9} + 24q^{11} - 16q^{14} - 20q^{16} + 30q^{19} - 32q^{26} + 4q^{29} + 36q^{36} + 10q^{39} - 24q^{41} + 36q^{46} - 42q^{49} + 48q^{51} + 76q^{56} - 132q^{59} + 24q^{61} - 56q^{64} + 28q^{69} - 24q^{71} - 32q^{74} - 156q^{76} + 64q^{79} - 40q^{81} - 24q^{84} + 96q^{89} - 86q^{91} + 24q^{94} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
975.2.w.a \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(-2\) \(0\) \(0\) \(-2\) \(q+(\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.b \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.c \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+\cdots\)
975.2.w.d \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(-\zeta_{12}-\zeta_{12}^{3})q^{7}+\cdots\)
975.2.w.e \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+(2\zeta_{12}+2\zeta_{12}^{3})q^{7}+\cdots\)
975.2.w.f \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(2\) \(q+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
975.2.w.g \(8\) \(7.785\) 8.0.56070144.2 None \(-2\) \(0\) \(0\) \(6\) \(q+(-\beta _{3}+\beta _{6}-\beta _{7})q^{2}-\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.h \(8\) \(7.785\) 8.0.191102976.5 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}+\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.i \(8\) \(7.785\) 8.0.191102976.5 None \(0\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{5}+\beta _{7})q^{2}-\beta _{6}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.j \(8\) \(7.785\) 8.0.56070144.2 None \(2\) \(0\) \(0\) \(-6\) \(q+(\beta _{3}-\beta _{6}+\beta _{7})q^{2}+\beta _{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
975.2.w.k \(24\) \(7.785\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)