Properties

Label 605.2.e
Level $605$
Weight $2$
Character orbit 605.e
Rep. character $\chi_{605}(362,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $92$
Newform subspaces $3$
Sturm bound $132$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 3 \)
Sturm bound: \(132\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 156 124 32
Cusp forms 108 92 16
Eisenstein series 48 32 16

Trace form

\( 92q + 8q^{3} + 8q^{5} + O(q^{10}) \) \( 92q + 8q^{3} + 8q^{5} - 36q^{12} + 12q^{15} - 20q^{16} - 16q^{20} - 36q^{23} - 20q^{25} + 48q^{26} - 4q^{27} - 8q^{31} - 36q^{36} - 4q^{37} - 40q^{38} + 60q^{42} + 8q^{45} + 20q^{47} - 64q^{48} - 4q^{53} - 32q^{56} + 64q^{58} + 152q^{60} - 68q^{67} + 16q^{70} + 48q^{71} - 28q^{75} - 84q^{78} - 112q^{80} + 68q^{81} - 44q^{82} + 8q^{86} - 16q^{91} - 20q^{92} - 76q^{93} + 56q^{97} + O(q^{100}) \)

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.e.a \(20\) \(4.831\) \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(4\) \(4\) \(0\) \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\)
605.2.e.b \(32\) \(4.831\) None \(0\) \(-4\) \(8\) \(0\)
605.2.e.c \(40\) \(4.831\) None \(0\) \(8\) \(-4\) \(0\)

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

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