Properties

Label 3150.2.g
Level $3150$
Weight $2$
Character orbit 3150.g
Rep. character $\chi_{3150}(2899,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $22$
Sturm bound $1440$
Trace bound $26$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 22 \)
Sturm bound: \(1440\)
Trace bound: \(26\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).

Total New Old
Modular forms 768 44 724
Cusp forms 672 44 628
Eisenstein series 96 0 96

Trace form

\( 44q - 44q^{4} + O(q^{10}) \) \( 44q - 44q^{4} - 4q^{11} - 4q^{14} + 44q^{16} - 16q^{19} - 12q^{26} + 16q^{29} - 40q^{31} + 28q^{34} - 44q^{41} + 4q^{44} - 16q^{46} - 44q^{49} + 4q^{56} + 20q^{59} + 36q^{61} - 44q^{64} + 24q^{71} + 16q^{74} + 16q^{76} - 56q^{79} + 56q^{86} - 36q^{89} + 20q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3150.2.g.a \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-6q^{11}+\cdots\)
3150.2.g.b \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4q^{11}+\cdots\)
3150.2.g.c \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.d \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.e \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-4q^{11}+\cdots\)
3150.2.g.f \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-3q^{11}+\cdots\)
3150.2.g.g \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2q^{11}+\cdots\)
3150.2.g.h \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}-2q^{11}+\cdots\)
3150.2.g.i \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+2iq^{13}+\cdots\)
3150.2.g.j \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-4iq^{13}+\cdots\)
3150.2.g.k \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}-iq^{13}+\cdots\)
3150.2.g.l \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}-2iq^{13}+\cdots\)
3150.2.g.m \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.n \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}-iq^{13}+\cdots\)
3150.2.g.o \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+2iq^{13}+\cdots\)
3150.2.g.p \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+2q^{11}+\cdots\)
3150.2.g.q \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}+iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.r \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.s \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.t \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+4q^{11}+\cdots\)
3150.2.g.u \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{7}+iq^{8}+4q^{11}+\cdots\)
3150.2.g.v \(2\) \(25.153\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(150, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(225, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(450, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)