Properties

Label 180.3.f
Level $180$
Weight $3$
Character orbit 180.f
Rep. character $\chi_{180}(19,\cdot)$
Character field $\Q$
Dimension $28$
Newform subspaces $8$
Sturm bound $108$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 180.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 20 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(108\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(7\), \(13\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(180, [\chi])\).

Total New Old
Modular forms 80 32 48
Cusp forms 64 28 36
Eisenstein series 16 4 12

Trace form

\( 28q - 4q^{4} + O(q^{10}) \) \( 28q - 4q^{4} + 8q^{10} + 36q^{14} - 44q^{16} + 12q^{20} + 20q^{25} - 60q^{26} - 136q^{34} - 20q^{40} + 96q^{41} - 204q^{44} + 164q^{49} - 168q^{50} + 180q^{56} - 56q^{61} + 260q^{64} + 168q^{70} + 564q^{74} - 168q^{76} + 372q^{80} - 40q^{85} - 168q^{86} - 192q^{89} - 360q^{94} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(180, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
180.3.f.a \(1\) \(4.905\) \(\Q\) \(\Q(\sqrt{-5}) \) \(-2\) \(0\) \(5\) \(4\) \(q-2q^{2}+4q^{4}+5q^{5}+4q^{7}-8q^{8}+\cdots\)
180.3.f.b \(1\) \(4.905\) \(\Q\) \(\Q(\sqrt{-5}) \) \(2\) \(0\) \(5\) \(-4\) \(q+2q^{2}+4q^{4}+5q^{5}-4q^{7}+8q^{8}+\cdots\)
180.3.f.c \(2\) \(4.905\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-6\) \(0\) \(q+iq^{2}-4q^{4}+(-3-2i)q^{5}-4iq^{8}+\cdots\)
180.3.f.d \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(0\) \(0\) \(0\) \(q+(-1-\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.e \(4\) \(4.905\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+(2+2\zeta_{12}^{2})q^{4}+\cdots\)
180.3.f.f \(4\) \(4.905\) \(\Q(i, \sqrt{15})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(4+\beta _{3})q^{4}+5\beta _{2}q^{5}+(3\beta _{1}+\cdots)q^{8}+\cdots\)
180.3.f.g \(4\) \(4.905\) \(\Q(\sqrt{-3}, \sqrt{22})\) None \(4\) \(0\) \(0\) \(0\) \(q+(1+\beta _{2})q^{2}+(-2+2\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
180.3.f.h \(8\) \(4.905\) 8.0.\(\cdots\).4 None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(180, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(180, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)