Properties

Label 975.2.bc
Level $975$
Weight $2$
Character orbit 975.bc
Rep. character $\chi_{975}(751,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $90$
Newform subspaces $14$
Sturm bound $280$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 975.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 14 \)
Sturm bound: \(280\)
Trace bound: \(7\)
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 90 214
Cusp forms 256 90 166
Eisenstein series 48 0 48

Trace form

\( 90q + q^{3} + 46q^{4} - 3q^{7} - 45q^{9} + O(q^{10}) \) \( 90q + q^{3} + 46q^{4} - 3q^{7} - 45q^{9} + 18q^{11} + 12q^{12} - 5q^{13} + 16q^{14} - 36q^{16} + 12q^{17} - 24q^{19} - 12q^{22} - 2q^{23} + 52q^{26} - 2q^{27} + 6q^{28} + 18q^{29} - 60q^{32} + 6q^{33} + 46q^{36} + 12q^{37} - 8q^{39} - 48q^{41} + 20q^{42} - 19q^{43} - 84q^{46} + 20q^{48} + 74q^{49} - 16q^{51} - 26q^{52} + 8q^{53} + 4q^{56} + 24q^{58} + 54q^{59} - 37q^{61} + 52q^{62} + 3q^{63} - 80q^{64} + 32q^{66} + 15q^{67} - 24q^{68} + 6q^{69} - 42q^{71} - 4q^{74} - 48q^{76} - 52q^{77} + 8q^{78} + 42q^{79} - 45q^{81} + 16q^{82} + 30q^{84} + 10q^{87} - 8q^{88} - 84q^{89} - 39q^{91} + 16q^{92} + 3q^{93} - 40q^{94} + 27q^{97} + 96q^{98} + O(q^{100}) \)

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.bc.a \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-1\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
975.2.bc.b \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(-3\) \(1\) \(0\) \(-3\) \(q+(-1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
975.2.bc.c \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(3\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(2-\zeta_{6})q^{7}+\cdots\)
975.2.bc.d \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(6\) \(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(4-2\zeta_{6})q^{7}+\cdots\)
975.2.bc.e \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-6\) \(q+(1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}+(-4+2\zeta_{6})q^{7}+\cdots\)
975.2.bc.f \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(3\) \(-1\) \(0\) \(3\) \(q+(1+\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
975.2.bc.g \(2\) \(7.785\) \(\Q(\sqrt{-3}) \) None \(3\) \(1\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
975.2.bc.h \(4\) \(7.785\) \(\Q(\zeta_{12})\) None \(6\) \(2\) \(0\) \(12\) \(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{2}q^{3}+\cdots\)
975.2.bc.i \(8\) \(7.785\) 8.0.56070144.2 None \(-6\) \(4\) \(0\) \(-6\) \(q+(-1-\beta _{2}+\beta _{5}+\beta _{6})q^{2}+\beta _{6}q^{3}+\cdots\)
975.2.bc.j \(8\) \(7.785\) 8.0.191102976.5 None \(0\) \(-4\) \(0\) \(-12\) \(q+(-\beta _{5}-\beta _{6})q^{2}-\beta _{1}q^{3}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)
975.2.bc.k \(12\) \(7.785\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(-6\) \(0\) \(3\) \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{6}q^{3}+(1-\beta _{2}+\beta _{6}+\cdots)q^{4}+\cdots\)
975.2.bc.l \(12\) \(7.785\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(6\) \(0\) \(-3\) \(q+\beta _{3}q^{2}+(1+\beta _{6})q^{3}+(-\beta _{6}-\beta _{10}+\cdots)q^{4}+\cdots\)
975.2.bc.m \(16\) \(7.785\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(-8\) \(0\) \(-6\) \(q+(-\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{3})q^{3}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
975.2.bc.n \(16\) \(7.785\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(8\) \(0\) \(6\) \(q+\beta _{5}q^{2}-\beta _{3}q^{3}+(1-\beta _{2}+\beta _{3}+\beta _{13}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)