Properties

Label 605.2.g
Level $605$
Weight $2$
Character orbit 605.g
Rep. character $\chi_{605}(81,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $144$
Newform subspaces $17$
Sturm bound $132$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.g (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 17 \)
Sturm bound: \(132\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

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

Total New Old
Modular forms 312 144 168
Cusp forms 216 144 72
Eisenstein series 96 0 96

Trace form

\( 144q + 6q^{2} + 4q^{3} - 32q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 30q^{9} + O(q^{10}) \) \( 144q + 6q^{2} + 4q^{3} - 32q^{4} - 6q^{6} + 4q^{7} - 2q^{8} - 30q^{9} - 8q^{10} + 12q^{12} - 2q^{13} + 4q^{14} - 6q^{15} - 20q^{16} + 12q^{17} - 14q^{18} - 14q^{19} + 8q^{20} + 32q^{21} - 8q^{23} - 38q^{24} - 36q^{25} + 12q^{26} - 20q^{27} + 2q^{28} - 10q^{29} + 20q^{30} + 8q^{31} - 28q^{32} - 32q^{34} + 12q^{35} - 26q^{36} - 20q^{37} + 30q^{38} - 30q^{39} + 6q^{40} - 4q^{41} - 10q^{42} - 4q^{43} + 38q^{46} + 4q^{47} + 34q^{48} - 14q^{49} + 6q^{50} - 14q^{51} + 54q^{52} - 12q^{53} + 24q^{54} - 180q^{56} + 50q^{57} + 6q^{58} + 58q^{59} - 26q^{60} - 4q^{61} + 68q^{62} - 26q^{63} - 12q^{64} - 16q^{65} + 24q^{67} - 46q^{68} + 30q^{69} - 28q^{70} - 8q^{71} + 64q^{72} + 10q^{73} - 68q^{74} - 6q^{75} - 16q^{76} - 140q^{78} - 54q^{79} - 8q^{80} - 32q^{81} - 22q^{82} - 2q^{83} - 24q^{84} + 16q^{85} + 58q^{86} - 68q^{87} - 48q^{89} + 26q^{90} - 96q^{91} - 60q^{92} - 8q^{93} - 50q^{94} + 16q^{95} - 6q^{96} - 88q^{97} + 68q^{98} + O(q^{100}) \)

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.g.a \(4\) \(4.831\) \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.b \(4\) \(4.831\) \(\Q(\zeta_{10})\) None \(-1\) \(3\) \(-1\) \(-3\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
605.2.g.c \(4\) \(4.831\) \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-1\) \(0\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{3}q^{4}+\cdots\)
605.2.g.d \(4\) \(4.831\) \(\Q(\zeta_{10})\) None \(1\) \(3\) \(-1\) \(3\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-3\zeta_{10}^{2}q^{3}+\cdots\)
605.2.g.e \(8\) \(4.831\) 8.0.13140625.1 None \(-3\) \(5\) \(2\) \(-4\) \(q-\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.f \(8\) \(4.831\) 8.0.64000000.2 None \(-2\) \(0\) \(2\) \(4\) \(q+(-1-\beta _{2}+\beta _{3}-\beta _{4}-\beta _{6})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.g \(8\) \(4.831\) 8.0.159390625.1 None \(-1\) \(1\) \(-2\) \(8\) \(q+(1-\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.h \(8\) \(4.831\) 8.0.324000000.3 None \(0\) \(-4\) \(-2\) \(0\) \(q+\beta _{7}q^{2}+2\beta _{6}q^{3}+\beta _{4}q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.i \(8\) \(4.831\) 8.0.324000000.3 None \(0\) \(2\) \(2\) \(0\) \(q+\beta _{7}q^{2}-\beta _{6}q^{3}+\beta _{4}q^{4}+(1+\beta _{2}+\cdots)q^{5}+\cdots\)
605.2.g.j \(8\) \(4.831\) 8.0.159390625.1 None \(1\) \(1\) \(-2\) \(-8\) \(q+(-1+\beta _{2}+\beta _{3}+\beta _{5}+\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
605.2.g.k \(8\) \(4.831\) 8.0.13140625.1 None \(2\) \(-5\) \(2\) \(1\) \(q+\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)
605.2.g.l \(8\) \(4.831\) 8.0.64000000.2 None \(2\) \(0\) \(2\) \(-4\) \(q+(-\beta _{2}+\beta _{7})q^{2}+2\beta _{1}q^{3}+(2\beta _{1}+2\beta _{3}+\cdots)q^{4}+\cdots\)
605.2.g.m \(8\) \(4.831\) 8.0.13140625.1 None \(3\) \(5\) \(2\) \(4\) \(q+\beta _{2}q^{2}+(1-\beta _{2}+\beta _{5}+\beta _{7})q^{3}+(1+\cdots)q^{4}+\cdots\)
605.2.g.n \(8\) \(4.831\) 8.0.159390625.1 None \(4\) \(1\) \(-2\) \(3\) \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
605.2.g.o \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-1\) \(-1\) \(3\) \(1\) \(q-\beta _{11}q^{2}+\beta _{8}q^{3}+(-\beta _{1}-3\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots\)
605.2.g.p \(12\) \(4.831\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(1\) \(-1\) \(3\) \(-1\) \(q+\beta _{9}q^{2}-\beta _{1}q^{3}+(-3+\beta _{3}+3\beta _{4}+\cdots)q^{4}+\cdots\)
605.2.g.q \(24\) \(4.831\) None \(0\) \(-6\) \(-6\) \(0\)

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

\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)