Properties

Label 3330.2.e
Level $3330$
Weight $2$
Character orbit 3330.e
Rep. character $\chi_{3330}(739,\cdot)$
Character field $\Q$
Dimension $96$
Newform subspaces $8$
Sturm bound $1368$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 3330 = 2 \cdot 3^{2} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3330.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(1368\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(7\), \(13\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3330, [\chi])\).

Total New Old
Modular forms 700 96 604
Cusp forms 668 96 572
Eisenstein series 32 0 32

Trace form

\( 96q + 96q^{4} + O(q^{10}) \) \( 96q + 96q^{4} + 2q^{10} + 8q^{11} + 96q^{16} + 22q^{25} - 20q^{26} - 12q^{34} + 2q^{40} - 8q^{41} + 8q^{44} + 28q^{46} - 92q^{49} + 96q^{64} + 4q^{65} - 16q^{70} + 40q^{71} - 16q^{85} - 20q^{86} + 44q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3330, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3330.2.e.a \(2\) \(26.590\) \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(4\) \(0\) \(q-q^{2}+q^{4}+(2-i)q^{5}+3iq^{7}-q^{8}+\cdots\)
3330.2.e.b \(2\) \(26.590\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-4\) \(0\) \(q+q^{2}+q^{4}+(-2+i)q^{5}+3iq^{7}+\cdots\)
3330.2.e.c \(10\) \(26.590\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(-10\) \(0\) \(-3\) \(0\) \(q-q^{2}+q^{4}+\beta _{5}q^{5}-\beta _{2}q^{7}-q^{8}+\cdots\)
3330.2.e.d \(10\) \(26.590\) \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None \(10\) \(0\) \(3\) \(0\) \(q+q^{2}+q^{4}-\beta _{5}q^{5}-\beta _{2}q^{7}+q^{8}+\cdots\)
3330.2.e.e \(16\) \(26.590\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}-\beta _{11}q^{5}-\beta _{14}q^{7}-q^{8}+\cdots\)
3330.2.e.f \(16\) \(26.590\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(2\) \(0\) \(q+q^{2}+q^{4}+\beta _{11}q^{5}-\beta _{14}q^{7}+q^{8}+\cdots\)
3330.2.e.g \(20\) \(26.590\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-20\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}+\beta _{10}q^{5}-\beta _{11}q^{7}-q^{8}+\cdots\)
3330.2.e.h \(20\) \(26.590\) \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(20\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta _{10}q^{5}-\beta _{11}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1665, [\chi])\)\(^{\oplus 2}\)