Properties

Label 2475.2.f
Level $2475$
Weight $2$
Character orbit 2475.f
Rep. character $\chi_{2475}(2276,\cdot)$
Character field $\Q$
Dimension $76$
Newform subspaces $9$
Sturm bound $720$
Trace bound $22$

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Defining parameters

Level: \( N \) \(=\) \( 2475 = 3^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2475.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(720\)
Trace bound: \(22\)
Distinguishing \(T_p\): \(2\), \(29\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2475, [\chi])\).

Total New Old
Modular forms 384 76 308
Cusp forms 336 76 260
Eisenstein series 48 0 48

Trace form

\( 76 q + 76 q^{4} + O(q^{10}) \) \( 76 q + 76 q^{4} + 84 q^{16} - 4 q^{22} + 32 q^{31} - 32 q^{34} - 68 q^{49} + 16 q^{58} + 92 q^{64} + 48 q^{67} - 112 q^{82} + 68 q^{88} - 16 q^{91} + 40 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(2475, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
2475.2.f.a \(2\) \(19.763\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+(-3+\beta )q^{11}+\cdots\)
2475.2.f.b \(2\) \(19.763\) \(\Q(\sqrt{-2}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}-q^{4}-\beta q^{7}+3q^{8}+(3+\beta )q^{11}+\cdots\)
2475.2.f.c \(2\) \(19.763\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}-\beta q^{7}-3q^{8}+(-3-\beta )q^{11}+\cdots\)
2475.2.f.d \(2\) \(19.763\) \(\Q(\sqrt{-2}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}-q^{4}+\beta q^{7}-3q^{8}+(3+\beta )q^{11}+\cdots\)
2475.2.f.e \(4\) \(19.763\) \(\Q(\sqrt{-2}, \sqrt{3})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+q^{4}-\beta _{3}q^{7}-\beta _{2}q^{8}+(2\beta _{1}+\cdots)q^{11}+\cdots\)
2475.2.f.f \(16\) \(19.763\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(1-\beta _{3})q^{4}+\beta _{5}q^{7}+(\beta _{9}+\cdots)q^{8}+\cdots\)
2475.2.f.g \(16\) \(19.763\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{9}q^{2}+(1-\beta _{3})q^{4}+\beta _{5}q^{7}+(\beta _{9}+\cdots)q^{8}+\cdots\)
2475.2.f.h \(16\) \(19.763\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+(\beta _{3}-\beta _{8}+\cdots)q^{7}+\cdots\)
2475.2.f.i \(16\) \(19.763\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{5}q^{2}+(2-\beta _{1})q^{4}-\beta _{15}q^{7}+(\beta _{4}+\cdots)q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(2475, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2475, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(495, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(825, [\chi])\)\(^{\oplus 2}\)