Properties

Label 605.2.j
Level $605$
Weight $2$
Character orbit 605.j
Rep. character $\chi_{605}(9,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $184$
Newform subspaces $11$
Sturm bound $132$
Trace bound $6$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 11 \)
Sturm bound: \(132\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).

Total New Old
Modular forms 312 248 64
Cusp forms 216 184 32
Eisenstein series 96 64 32

Trace form

\( 184q + 44q^{4} + 3q^{5} + 18q^{6} + 26q^{9} + O(q^{10}) \) \( 184q + 44q^{4} + 3q^{5} + 18q^{6} + 26q^{9} + 16q^{14} + 13q^{15} - 40q^{16} - 6q^{19} + 4q^{20} - 8q^{21} - 6q^{24} + 13q^{25} - 84q^{26} - 2q^{29} - 26q^{30} - 2q^{31} - 80q^{34} - 22q^{35} - 2q^{36} - 30q^{39} - 12q^{40} + 52q^{41} - 84q^{45} + 62q^{46} - 28q^{50} + 42q^{51} + 40q^{54} - 12q^{56} + 4q^{59} + 90q^{60} + 40q^{61} - 28q^{64} + 40q^{65} - 36q^{69} + 18q^{70} - 54q^{71} - 48q^{74} - 21q^{75} - 56q^{76} - 38q^{79} + 16q^{80} - 42q^{81} - 12q^{84} - 58q^{85} - 6q^{86} - 144q^{89} - 78q^{90} + 28q^{91} - 14q^{94} - 48q^{95} + 86q^{96} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
605.2.j.a \(8\) \(4.831\) 8.0.484000000.6 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(-10\) \(0\) \(q+(\beta _{1}-\beta _{4})q^{2}+(1+\beta _{2}-3\beta _{3}+3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.b \(8\) \(4.831\) 8.0.228765625.1 \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(-3\) \(0\) \(q+(-\beta _{4}-2\beta _{5})q^{3}+(-2+2\beta _{3}+2\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.j.c \(8\) \(4.831\) 8.0.484000000.6 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(10\) \(0\) \(q+(\beta _{1}-\beta _{6})q^{2}+(-2\beta _{2}+2\beta _{3}-3\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.j.d \(16\) \(4.831\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+(\beta _{1}-\beta _{12}-\beta _{13})q^{2}+(-\beta _{5}-\beta _{13}+\cdots)q^{3}+\cdots\)
605.2.j.e \(16\) \(4.831\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}+\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.f \(16\) \(4.831\) 16.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{12}q^{2}-\beta _{3}q^{3}-\beta _{10}q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.j.g \(16\) \(4.831\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{13}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.j.h \(16\) \(4.831\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) \(q+\beta _{13}q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+(\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.j.i \(16\) \(4.831\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(3\) \(0\) \(q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots\)
605.2.j.j \(16\) \(4.831\) 16.0.\(\cdots\).1 None \(0\) \(0\) \(3\) \(0\) \(q+(\beta _{1}+\beta _{4}+\beta _{5}-\beta _{8}+\beta _{11}-\beta _{13}+\cdots)q^{2}+\cdots\)
605.2.j.k \(48\) \(4.831\) None \(0\) \(0\) \(6\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)